Final answer:
The discriminant of the equation 4x^2+16x+16=0 is 0, indicating that there is one real, repeated root.
Explanation:
To find the discriminant and the number of real roots for the equation 4x^2+16x+16=0, we first recognize it as a quadratic equation of the form ax^2+bx+c=0. The discriminant of a quadratic equation is given by the formula b^2-4ac. In our equation, a=4, b=16, and c=16. Substituting these values into the formula gives us 16^2 - 4(4)(16), which simplifies to 256 - 256, yielding a discriminant of 0. A discriminant of 0 indicates that there is exactly one real root, which is also a repeated or double root.
Which right triangle prism has the greatest volume
Answer:
the second option (9,11,8)
Step-by-step explanation:
The PE class has 12 boys and 8 girls. What is the maximum number of teams that the teacher can divide the class into so that each team has an equal number of boys and girls, the greatest common factor of the numbers of girls and boys? Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 8: 1, 2, 4, 8
2
4
24
96
Answer:
4
Step-by-step explanation:
12 can be multipled by 4 and 4 and 8 can be multipled by 4 and 2 so 4 is the greatest common factor
Answer:
4
Step-by-step explanation:
Simplify (b^4)^3. ❤️ SLAT*_^}
Answer:
[tex]b^1^2[/tex]
Step-by-step explanation:
First, multiply by exponent rule.
[tex](x^y)^z=x^y^z[/tex]
[tex]b^4^*^3[/tex]
Then, multiply by the numbers from left to right.
[tex]4*3=12[/tex]
[tex]b^1^2[/tex], is the correct answer.
Answer:
b^12
Step-by-step explanation:
When there is a power of a power, you multiply the powers
Find the value of ax 4 ; a = 2, x = 1.
Select one: a. 2 b. 4 c. 1 d. 8
For this case we have the following expression:
[tex]ax ^ 4[/tex]
We must find the value of the expression when:
[tex]a = 2\\x = 1[/tex]
Substituting the values in the expression we have:
[tex]2 (1) ^ 4 = 2 * 1 = 2[/tex]
Thus, the value of the expression is 2.
Answer:
The value of the expression is 2
Option A
Answer:
The correct answer is A
Step-by-step explanation:
The given expression is [tex]ax^4[/tex].
We want to evaluate this expression for: [tex]a=2,x=1[/tex].
We just have to substitute a=2 wherever we see 'a' in the expression [tex]ax^4[/tex] and x=1 wherever see x in the same expression.
We perform the substitution to get:
[tex]2(1)^4[/tex]
We evaluate the exponent to get:
[tex]2(1)[/tex]
We now multiply to get:
[tex]2[/tex]
Solve this equation: 8p = -96
p=
8p = -96
Because that Moderator want me to explain this, so,
devid by 8 from both side:
8p / 8 = -96 / 8
p = -12
And that is the answer:
P = -12
Write the equation 0.3x2 + 5x - 7 =0 in general form and then choose the value of "b."
For this case we have that by definition, an equation of the second degree is given by:
[tex]ax ^ 2 + bx + c = 0[/tex]
We have the following equation:
[tex]0.3x ^ 2 + 5x-7 = 0[/tex]
Then, according to the definition above, we have to:
[tex]a = 0.3\\b = 5\\c = -7[/tex]
Thus, b equals 5.
Answer:
[tex]b = 5[/tex]
Option C
In a circle graph, a section that represents 80% of the graph has a central angle measure of what? 72° 146° 288° 360°
Answer:
288°
Step-by-step explanation:
80% of a circle is
80% of 360 degree
.80 *360
288
Answer:
C. 288°
Step-by-step explanation:
80% · 360° (convert 80% to a decimal)
= 0.8 · 360° (then multiply 0.8 to 360°)
= 288°
Which equation represents a line that passes through (2, –0.5) and has a slope of 3?
Answer:
y + 0.5 = 3(x - 2).
Step-by-step explanation:
We use the point-slope form of the equation which is y - y1 = m(x - x1).
Here m = 3 , x1 = 2 and y1 = -0.5, so the equation is:
y - (-0.5) = 3(x - 2)
y + 0.5 = 3(x - 2).
which statement best describes a line in slope intercept form when the coefficient of the x term is negative
Answer:
The angle made by line with positive x axis is more than 90°
Step-by-step explanation:
A line is represented in slope intercept form as
y=mx+c
Where m is called the slope of the line and c is called the y intercept .
Here by slope we means the tangent of the angle , the line makes with the positive x axis .
Now in the case when the coefficient of x is negative , that means the tangent of the angle which line makes with the positive direction of x axis is negative
or
tan [tex]\theta[/tex] = negative
[tex]\theta[/tex] > 90
that means our line makes an obtuse angle that is more than 90° with the positive x axis.
Answer:
the line slants up
Step-by-step explanation:
Which equation represents the line shown on the graph?
1. y=x+2
2. y=-2x
3. y=2x
4. y=-x+2
Answer:
4
Step-by-step explanation:
Recall that the equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept.
we can see that the slope is negative (i.e graph goes from top left to bottom right). hence the value for m must be negative.
By looking at the answer choices, only 2 and 4 have negative x-terms, hence we can ignore 1 and 3.
Also we notice that the graph intersects the y-axis at y = 2, hence the y-intercept must be 2.
Only Answer 4 satisfies both requirements and is the correct answer.
What is the value of x if 9x^-1 - 2 = 25
Answer: [tex]x=\frac{1}{3}[/tex]
Step-by-step explanation:
You need to remember the Negative exponent rule:
[tex]a^{-n}=\frac{1}{a^n}[/tex]
Then, having the equation [tex]9x^{-1} - 2 = 25[/tex], you can rewrite it in this form:
[tex]\frac{9}{x} - 2 = 25[/tex]
Now add 2 to both sides of the equation:
[tex]\frac{9}{x} - 2+2 = 25+2\\\\\frac{9}{x}=27[/tex]
Multiply both sides of the equation by "x":
[tex](x)(\frac{9}{x})=27(x)\\\\9=27x[/tex]
And finally divide both sides of the equation by 27.
The value of "x" is:
[tex]x=\frac{9}{27}\\\\x=\frac{1}{3}[/tex]
Answer:
C on edg
Step-by-step explanation:
Select the correct answer.
Which transformation of the red triangle on the graph maps it onto the missing piece of the square?
Answer:
The above answer is incorrect.
Step-by-step explanation:
The answer would be Option D.
A clockwise rotation about the origin basically means turning the shape 90°, and moving it to the left (in this scenario.)
We see that the red triangle is in the first quadrant, and that the green polygon is in the second quadrant. If we rotate the red triangle about the origin clockwise, it would be perfectly in the missing portion of the green square, making is a perfect square.
Which of the following is a solution of y - x < -3?
A. (6, 2)
B. (2, 6)
C. (2, -1)
For this case we have the following inequality:
[tex]y-x <-3[/tex]
We must evaluate each of the points and verify if the inequality is met:
[tex](6,2)\\2-6 <-3\\-4 <-3[/tex]
The inequality is met!
[tex](2,6)\\6-2 <-3\\4 <-3[/tex]
It is not fulfilled!
[tex](2, -1)\\-1-2 <-3\\-3 <-3[/tex]
It is not fulfilled!
Thus, the point that meets the inequality is (6,2)
Answer:
Option A
The domain of the following relation: R: {(-3, 4), (5,0), (1, 5), (2, 8), (5, 10)} is (1 point)
{-3, 1, 2, 5)
{4, 0, 5, 8, 10)
{-3, 5, 1, 2,5}
No domain exists
Answer:
{-3,1,2,5}
Step-by-step explanation:
The domain is the input values
(-3,1,5,2,5)
We only list the 5 one time
{-3,1,2,5}
Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.
Answer:
∠1 = ∠4 and ∠3 = ∠5 ( alternate interior angle).
Step-by-step explanation:
Given : Triangle ABC with angle 1, 2, 3.
To find : Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.
Solution : We have given that triangle ABC with angle 1, 2, 3.
Here, line DE and AC are parallel and BA is traversal line.
∠1 = ∠4 ( alternate interior angle)
∠3 = ∠5 ( alternate interior angle)
∠4 + ∠2+ ∠5 = 180 ( angle formed on line)
∠1 + ∠2 + ∠3 = 180.
Therefore, ∠1 = ∠4 and ∠3 = ∠5 ( alternate interior angle).
The angles in a triangle add up to 180 degrees.
The text that completes the proof is: alternate interior angle
From the question, we can see that the missing statement is on the 4th line
Where:
[tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex]
From the figure of the triangle, we can see that:
[tex]\angle 1[/tex] and [tex]\angle 4[/tex] are alternate interior angles[tex]\angle 5[/tex] and [tex]\angle 3[/tex] are alternate interior anglesHence, the statement that completes the proof is: alternate interior angle
Read more about the proofs of angles in a triangle at:
https://brainly.com/question/20441035
The South Company cash account had a balance of $1,202.50 on January 31. A deposit, made on the 31st, in the amount of $100.05 was in transit. The January 31 bank statement presented the following information.
Bank statement balance $1,421.95
NSF charge 18.00
Bank service charge 8.50
Note collected 150.00
South also had outstanding checks in the amount of $196.00. What was South’s reconciled balance?
$1,202.50
$1,326.00
$1,271.95
$1,236.00
Answer:
$1326
Step-by-step explanation:
Follow the format of the reconciliation statement
The adjusted cash balances should match
Cash balance as per the bank statement, January 31 1421.95
Add: Deposit in transit 100.05
Deduct: Outstanding checks (196)
Adjusted cash balance 1326
Balance as per depositor's record, January 31 1202.5
Subtract: NSF check (18)
Subtract: Service charges (8.5)
Add: receivable collected 150
Adjusted cash balance 1326
The reconciled amount is $1326.
!!
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (sºt)(-7)?
Answer:
- 439Step-by-step explanation:
[tex]s(x)=2-x^2,\ t(x)=3x\\\\(s\circ t)(x)=s\bigg(t(x)\bigg)-\text{exchange x to t(x) = 3x:}\\\\(s\circ t)(x)=2-(3x)^2=2-3^2x^2=2-9x^2\\\\(s\circ t)(-7)-\text{put x = -7 to the equation:}\\\\(s\circ t)(-7)=2-9(-7)^2=2-9(49)=2-441=-439[/tex]
Answer:
-439
Step-by-step explanation:
Got it right on edge
Which expression is equivalent to 4√24x6y/128x4y5? Assume x ≠ 0 and y > 0.
For this case we must simplify the given expression:
Rewriting we have:
[tex]\sqrt [3] {\frac {2 * 5x ^ 5} {2 * 27x ^ 8}} =\\\sqrt [3] {\frac {5x ^ 5} {27x ^ 8}} =[/tex]
By definition of division of powers of equal base, the same base is placed and the exponents are subtracted:
[tex]\sqrt [3] {\frac {5x ^ {5-8}} {27}} =\\\sqrt [3] {\frac {5x ^ {- 3}} {27}} =\\\sqrt [3] {\frac {5} {27x ^ 3}} =[/tex]
We have to:
[tex]\sqrt [3] {27x ^ 3} = 3x[/tex]
Then, the expression is reduced to:
[tex]\frac {\sqrt [3] {5}} {3x}[/tex]
ANswer:
Option D
Answer:
its D jus trust
Step-by-step explanation:
Please some one help me
Hello There!
To find the quotient of [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{8}[/tex],
we need to multiply by the reciprocal meaning that the fraction
[tex]\frac{3}{4}[/tex] stays the same but we flip the numerator and
denominator for our second fraction so it will end up being
[tex]\frac{8}{1}[/tex] which is the same thing as 8 so the second choice
is your answer.
19. A school has 24 teachers. Of those teachers,
18 bought lunch today. What percent
of the teachers bought lunch today?
Answer: 75%
Step-by-step explanation:
To get the answer we will divide the amount of teachers that bought lunch by the total amount of teachers
18/24 = 75%
Answer:
75
Step-by-step explanation:
if you put it in a fraction you will get 18 over 24 and to find a percent you divided by numerator by denominator so you divide 18 by 24 and get 0.75
candy has to paint a fence. if she can paint 2/3 of each section in 1/2 hour, and there are 9 sections , how long will it take her to paint the entire fence?
[tex]6 \frac{3}{4}[/tex] hours
Step-by-step explanation:First, find the time it takes to paint each section with this formula: [tex]\frac{\frac{1}{2}}{\frac{2}{3}}[/tex]
You can use keep, change, flip, to make this multiplication. [tex]\frac{1}{2} * \frac{3}{2}[/tex]
Multiply the numerators. [tex]1 * 3 = 3[/tex]
Multiply the denominators. [tex]2 * 2 = 4[/tex]
So, it takes [tex]\frac{3}{4}[/tex] hour to paint one section of fence.
Now, we just need to find how long it takes to paint 9 sections. [tex]9 * \frac{3}{4}[/tex]
Multiply. [tex]\frac{27}{4}[/tex]
Finally, simplify. [tex]6 \frac{3}{4}[/tex]
Find the least common denominator for these
two rational expressions,
Answer:
(y + 2)²(y + 4)
Step-by-step explanation:
Factor the denominators of both fractions
y² + 4y + 4 = (y + 2)²
y² + 6y + 8 = (y + 2)(y + 4)
The least common denominator is (y + 2)²(y + 4)
Answer:
Step-by-step explanation:
y²+4y+4=(y+2)² =(y+2)(y+2)
y²+6y+8 = (y+2)(y+4)
the least common denominator for these
two rational expressions is : (y+2)²(y+4)
The equation y-3=-2(x+5) is written in point-slope form. What is the y-intercept of the line?
Answer:
y = - 7
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 )
Given
y - 3 = - 2(x + 5) ← distribute right side
y - 3 = - 2x - 10 ( add 3 to both sides )
y = - 2x - 7 ← in slope- intercept form
with y- intercept c = - 7
y = - 7 is the y-intercept of the line.
What is equation of line?A line's equation has the conventional form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.
Given
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y - 3 = - 2(x + 5) ← distribute right side
y - 3 = - 2x - 10 ( add 3 to both sides )
y = - 2x - 7 ← in slope- intercept form
with y- intercept c = - 7
To know more about equation of line refer to :
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The point(0,2) Is the only solution to the system of linear equations that contains the equations Y = 1/2 X +2 and y =-3X +2. Choose the term that describes a set of equations
a)dependent equations
b) inconsistent equations
C)independent equations
D) cannot be determined
Answer:
independent equations
Choice C is correct
Step-by-step explanation:
The system of linear equations that contains the equations;
Y = 1/2 X +2 and y =-3X +2 is said to be consistent since it has at least one solution;
The point (0,2)
If a consistent system of equations has exactly one solution, it is said to be independent.
Final answer:
The correct term describing a set of equations where each equation represents a different line that intersects at only one point is 'independent equations'.
Explanation:
The point (0,2) is mentioned as the only solution to the system of linear equations with equations y = 1/2x + 2 and y = -3x + 2. Since both equations have only one point of intersection, this means that the graphs of the two equations are two different lines that intersect at exactly one point. This means the system is consistent and the equations are independent, as they form two different lines.
Therefore, the term that describes a set of equations where each equation represents a straight line and they intersect at exactly one point is independent equations.
What is eleven p.m plus six hours
Answer:
5 a.m.
Step-by-step explanation:
From 11 p.m. to midnight is 1 hour. Adding 5 hours to this result is equivalent to "eleven p.m plus six hours" and is 5 a.m.
The area of the indoor sports exhibition is shown below.
What is its perimeter?
m
What is its area?
Answer:
Step-by-step explanation:
The perimeter of the circular part of the sports exhibition can be found with the formula [tex]\pi[/tex]r.The equation is halved from the 2[tex]\pi[/tex]r as it is half a circle.
perimeter of circular part=17[tex]\pi[/tex]
Perimeter of the sports exhibition:
(4000/100)+10+10+68+33+17[tex]\pi[/tex]+34+(700/100)
=202+17[tex]\pi[/tex]
=255m(nearest whole number)
For the area, find the total area of the representive shapes
The two rectangles:10*40+68*33
=2644
The area of the semi circle (:[tex]\pi[/tex]r^2)/2
=17*17*[tex]\pi[/tex]/2
=144.5 [tex]\pi[/tex]
Total area:
2644+144.5 [tex]\pi[/tex]
=3098m^2(nearest whole number)
If f(x) = 4x + 7, which of the following is the inverse of f(x)?
O A. f-'(x) = 4x - 7
O B. f'() = *=4
C. FGx) = 7 - 4x
O D. F"(x) = *z?
For this case we must find the inverse of the following function:
[tex]f (x) = 4x + 7[/tex]
For it:
Replace f (x) with y:
[tex]y = 4x + 7[/tex]
We exchange the variables:
[tex]x = 4y + 7[/tex]
We solve for y:
We subtract 7 on both sides of the equation:
[tex]x-7 = 4y[/tex]
We divide between 4 on both sides of the equation:
[tex]y = \frac {x} {4} - \frac {7} {4}[/tex]
Finally, we change y by[tex]f ^ {- 1} (x)[/tex]:
[tex]f ^ {- 1} (x) = \frac {x} {4} - \frac {7} {4}[/tex]
ANswer:
[tex]f ^ {- 1} (x) = \frac {x} {4} - \frac {7} {4}[/tex]
the inverse function f-1(x) is (x - 7) / 4, which matches option B: f-1(x) = (x / 4) - (7 / 4).
The student asks which of the provided options is the inverse of the function f(x) = 4x + 7. To find the inverse function, we usually swap x and y and then solve for y. The steps to find the inverse are:
Replace f(x) with y: y = 4x + 7.Swap x and y: x = 4y + 7.Solve for y: y = (x - 7) / 4.Therefore, the inverse function f-1(x) is (x - 7) / 4, which matches option B: f-1(x) = (x / 4) - (7 / 4).
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and across the x-axis to obtain point C. What are the coordinates of points B and C?
ANSWER
[tex]B(2,-3)[/tex]
[tex]C(-2,3)[/tex]
EXPLANATION
The given point has coordinates A(-2,-3).
The rule for the reflection across the y-axis is
[tex](x,y)\to(-x,y)[/tex]
We apply this rule to obtain the coordinates of B.
[tex]A(-2,-3)\to B(--2,-3)[/tex]
Simplify the coordinates of B to get:
[tex]A(-2,-3)\to B(2,-3)[/tex]
The rule for reflection across the x-axis is
[tex](x,y)\to (x,-y)[/tex]
When the point A(-2,-3) is reflected across the x-axis to obtain C, then the coordinates of C are:
[tex]A(-2,-3)\to C(-2,--3)[/tex]
[tex]A(-2,-3)\to C(-2,3)[/tex]
Answer:
B(2 ,-3) and C( -2, 3)
Step-by-step explanation:
i did the test lol :)
Giving 20 points please get it right
Answer:
B and C option is the answer to this question
Step-by-step explanation:
Jeremy wants to determine the number of solutions for the equation below without actually solving the equation.
Answer:
Determine if the equation has the form x = a, if it does then it has one solution.
Step-by-step explanation:
We are given the following equation for which Jeremy wants to determine the number of solutions without actually solving the equation.
The best method for this would be to determine if the equation has the form [tex]x=a[/tex] where [tex]x[/tex] represents the variable while [tex]a[/tex] represents the constant.
If the equation has this form, then it means it has one solution.
Answer:
C or
Determine whether the equation has the form x = a, and if it does, the equation has one solution.
Step-by-step explanation:
i just took the test