Answer:
[tex]a=\pm i\sqrt{26}}[/tex]
Step-by-step explanation:
[tex]6^2+a^2=10\\\\36+a^2=10\qquad\text{subtract 36 from both sides}\\\\a^2=-26<0\\\\\bold{NO\ REAL\ SOLUTIONS}\\\\\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\a^2=-26\to a=\pm\sqrt{-26}\\\\a=\pm\sqrt{(-1)(26)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\a=\pm\sqrt{-1}\cdot\sqrt{26}\\\\a=\pm i\sqrt{26}[/tex]
Given the functions k(x) = 2x^2 − 5 and p(x) = x − 3, find (k ∘ p)(x).
a. (k ∘ p)(x) = 2x^2 − 6x + 4
b. (k ∘ p)(x) = 2x^2 − 12x + 13
c. (k ∘ p)(x) = 2x^2 − 12x + 18
d. (k ∘ p)(x) = 2x2 − 8
Answer:
(k ∘ p)(x)=2x^2-12x+13
Step-by-step explanation:
(k ∘ p)(x)=k(p(x))
(k ∘ p)(x)=k(x-3)
(k ∘ p)(x)=2(x-3)^2-5
(k ∘ p)(x)=2(x-3)(x-3)-5
Use foil on (x-3)(x-3) or use this as a formula:
(x+a)^2=x^2+2ax+a^2.
(k ∘ p)(x)=k(p(x))
(k ∘ p)(x)=k(x-3)
(k ∘ p)(x)=2(x-3)^2-5
(k ∘ p)(x)=2(x-3)(x-3)-5
(k ∘ p)(x)=2(x^2-6x+9)-5
Distribute: multiply terms inside ( ) by 2:
(k ∘ p)(x)=2x^2-12x+18-5
(k ∘ p)(x)=2x^2-12x+13
The composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]
Option b is correct.
Composite function :
Given function are,
[tex]k(x)=2x^{2} -5,p(x)=(x-3)[/tex]
We have to find composite function [tex]k(p(x))[/tex].
[tex]k(p(x))=k(x-3)\\\\k(p(x))=2(x-3)^{2}-5\\ \\k(p(x))=2(x^{2} +9-6x)-5\\\\k(p(x))=2x^{2} +18-12x-5\\\\k(p(x))=2x^{2} -12x+13[/tex]
Thus, the composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]
Learn more about the composite function here:
https://brainly.com/question/10687170
What are the zeros of the function below? Check all that apply.
F(x)= (x - 2)(x + 1)/x(x - 3)(x + 5)
The zeros of the function are 2 and -1.
Zeros of function:The zeros of a function are the values of x when f(x) is equal to 0.
Given function is, [tex]f(x)=\frac{(x-2)(x+1)}{x(x-3)(x+5)}[/tex]
Equate given function to zero.
[tex]\frac{(x-2)(x+1)}{x(x-3)(x+5)} =0\\\\(x-2)(x+1)=0\\\\x=2,x=-1[/tex]
Learn more about the Zeros of function here:
https://brainly.com/question/446160
There are 42 boys and 48 girls in the sixth grade and each student must be assigned a homeroom. Each homeroom should have the same number of boys and the same number of girls.
What is the greatest possible number of sixth-grade homerooms?
A
8
B
6
C
4
The most significant number of homerooms that can be created with an equal number of boys and girls in each is 6.
Explanation:To answer this question, we need to find the greatest common divisor (GCD) for the number of boys and girls. The GCD is the most significant number that can divide both numbers equally. The GCD of 42 (number of boys) and 48 (number of girls) is 6.
Therefore, the sixth grade's most significant possible number of homerooms would be 6, with each homeroom having seven boys and eight girls.
Learn more about Greatest Common Divisor here:https://brainly.com/question/23270841
#SPJ3
slope intercept form of equation of a line that passes through (-3,8) y=-2/3x+6 what is the point slope equation for this line???
Answer:
[tex]\large\boxed{y-8=-\dfrac{2}{3}(x+3)}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the equation of a line in the slope-intercept form
[tex]y=-\dfrac{2}{3}x+6\Rightarrow m=-\dfrac{2}{3}[/tex]
and the point (-3, 8).
Substitute:
[tex]y-8=-\dfrac{2}{3}(x-(-3))\\\\y-8=-\dfrac{2}{3}(x+3)[/tex]
A triangle has two sides of lengths 4 and 5. What value could the length of the third side be?
Answer:
2, 3, 4, 5, 6, 7 or 8.
Step-by-step explanation:
We know that the sum of two sides on a triangle should ALWAYS be greater than the third side. Then we have:
5-4 < x < 5 + 4
1 < x < 9
Therefore, the lenght of the third side could be any number between 1 and 9. If the lenght of the third side is an integrer, then the lenght could be:
2, 3, 4, 5, 6, 7 or 8.
Answer:
The length of the third side could be all real numbers greater than 1 unit and less than 9 units
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
Applying the triangle inequality theorem
Let
x ----> the length of the third side
1) 4+5 > x
9 > x
Rewrite
x < 9 units
2) 4+x > 5
x > 5-4
x > 1 units
therefore
The solution for the third side is the interval -----> (1,9)
All real numbers greater than 1 unit and less than 9 units
therefore
The length of the third side could be all real numbers greater than 1 unit and less than 9 units
The variable z is directly proportional to x. When x is 15, z has the value 165. What is the value of z when x = 25?
Answer:
z=275
Step-by-step explanation:
it has a ratio 1:11
that must be it
Answer:
275
Step-by-step explanation:
z is directly proportional to x:
z = kx
When x is 15, z is 165.
165 = k × 15
k = 11
When x = 25:
z = 11 × 25
z = 275
The function f(x) = 10(5)x represents the growth of a lizard population every year in a remote desert. Crista wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Crista's purposes? (1 point)
f(x) = 10(52) the x over 2 power
f(x) = ten halves (5)x
f(x) = 10(5)x
f(x) = 10( 5 to the one half power )2x
Answer:
[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex] (first option)
Step-by-step explanation:
we have
[tex]f(x)=10(5)^{x}[/tex]
where
x ----> is the time in years
we know that
Crista wants to manipulate the formula to an equivalent form that calculates every half-year
The exponent will be
x/2 -----> the time every half year
To find an equivalent form
[tex]f(x)=10(5^{a})^{\frac{x}{2}}[/tex]
[tex]10(5)^{x}=10(5^{a})^{\frac{x}{2}}[/tex]
[tex]10(5)^{x}=10(5)^{a\frac{x}{2}}[/tex]
so
[tex]x={a\frac{x}{2}}[/tex]
[tex]a=2[/tex]
The equivalent form is
[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex]
Find distance in units from Point A (4,2) to Point B (-3,2)?
Answer:
using distance formula or graphing you can find your answer
Step-by-step explanation:
(7,0) from 4 to -3 is -7. Take the absolute vale of -7 and you get 7.
Hope i helped :)
Answer:
Distance from A to B = 7 units
Step-by-step explanation:
We are given the following two points and we are to find the distance between them:
A (4,2)
B (-3,2)
We will be using the distance formula for this:
Distance = [tex] \sqrt { ( x _ 2 - x _1)^ 2 + ( y _ 2 - y _ 1 ) ^ 2 } [/tex]
AB = [tex]\sqrt{(-3-4)^2+(2-2)^2} = \sqrt{49}[/tex] = 7 units
graph the function f(x)=(13)x−1 ?
Answer:
Step-by-step explanation:
For this case we must graph the following function:
[tex]f (x) = 13x-1[/tex]
We found the cut points:
Cutting point with the y-axis:
We make [tex]x = 0,[/tex]
[tex]y = 13 (0) -1\\y = 0-1\\y = -1[/tex]
Cutting point with the x axis:
[tex]0 = 13x-1\\1 = 13x\\x = \frac {1} {13} = 0.078[/tex]
It is observed that the line has a positive slope, [tex]m = 13[/tex]
The graph is seen in the attached image.
Answer:
See attached image
What is the solution to this equation?
x + 4(x + 5) = 40
O A. x= 12
O B. x = 7
O c. x= 9
O D. x= 4
On a map 1/8 of an inch stands for 24 miles. On this map two cities are 2.5 inches apart. What is the actual distance between cities
Answer:
The actual distance between the cities is 480 miles.
Step-by-step explanation:
2.5 inches is 20/8 inches, multiply 20 by 24 miles which gives you 480.
Answer:
480 miles.
Step-by-step explanation:
By proportion the actual distance is
(2.5 / 1/8) * 24
= (2.5 / 0.125) * 24
= 20 * 24
= 480 miles.
The compound probability of two events, E and F, is ; the probability of E is and of F is . In two or more complete sentences, explain why E and F are not independent.
Answer:
Events E and F are not independent if the probability of event E occurring is affecting the probability of event F occurring.
Step-by-step explanation:
Two events are independent when the probability of one event occurring has no connection with that of the other event.
Example, when you toss a coin and roll a six sided die, the probability of getting a head or a tail has no connection with the probability of getting any number face.A real life example will be the probability going to the mall and owning a cat at home.These two have no influence on one another.
Mathematically independent events can be calculated as;
P(E∩F)=P(E)-P(F)
HELP ASAP! I don’t under stand this.
Answer:
8/17
Step-by-step explanation:
Since this is a right triangle, we can use the trigonometric identities
sin Y = opposite side/ hypotenuse
= 16/34
Dividing the top and bottom by 2
= 8/17
Pls help ?????? Thank u all
Answer:
The graph in the attached figure ( is the third option)
Step-by-step explanation:
we have the compound inequality
[tex]-18> -5x+2\geq -48[/tex]
Divide the compound inequality in two inequalities
[tex]-18> -5x+2[/tex] -----> inequality A
[tex]-5x+2\geq -48[/tex] -----> inequality B
Step 1
Solve inequality A
[tex]-18> -5x+2[/tex]
[tex]-18-2> -5x[/tex]
[tex]-20> -5x[/tex]
Multiply by -1 both sides
[tex]20<5x[/tex]
[tex]4<x[/tex]
Rewrite
[tex]x > 4[/tex]
The solution of the inequality A is the interval ------>(4,∞)
Step 2
Solve the inequality B
[tex]-5x+2\geq -48[/tex]
[tex]-5x\geq -48-2[/tex]
[tex]-5x\geq -50[/tex]
Multiply by -1 both sides
[tex]5x\leq 50[/tex]
[tex]x\leq 10[/tex]
The solution of the inequality B is the interval -----> (-∞,10]
therefore
The solution of the compound inequality is
(4,∞) ∩ (-∞,10]=(4,10]
All real numbers greater than 4 (open circle) an less than or equal to 10 (close circle)
The solution in the attached figure
A ski club charges a $45 membership fee plus $18 to rent ski equipment per day. Which of the following equation can be used to find the total cost of membership at the club, when renting equipment for X days?
Answer:
[tex]y = 18x + 45[/tex]
Step-by-step explanation:
You can use a linear equation of the form
[tex]y = mx + b[/tex] to represent the situation.
where b is the constant amount represented by the intercept with the y-axis, in this case b e is the cost of membership.
m is the slope, and in this case it is the cost per day of renting a team for x days.
y is the total cost of membership at the club, when renting equipment for X days
So the linear equation is:
[tex]y = 18x + 45[/tex]
which of the segments below is a secant
Answer:
B
Step-by-step explanation:
A secant is a line which intersects a circle at 2 points
From the diagram this is XY → B
The correct option is option B: The line segment XY is a secant.
What is secant?Line segment which intersects the circle at two points is called secant.
We are given circle with center at O.
From the options,
1. Line UZ :
UZ intersects the circle at one point. So it can't be secant.
2. Line XY:
XY intersects the circle at TWO points. So it is a secant.
3. Line XO :
XO intersects the circle at one point. So it can't be secant.
Therefore the line segment XY is a secant.
Learn more about secant
here: https://brainly.com/question/2375441
#SPJ2
The floor of a room measures 5 meters by 7 meters. A carpet sells 285 pesos per square meter. How much would it cost to carpet the room?
Find the area of the rug by multiplying the length by the width:
7 x 5 = 35 square meters.
Now multiply the area of the rug by the cost:
35 square meters x 285 pesos per square meter = 9,975 total pesos.
A polynomial has been factored below, but some constants are missing.
3x^3+6x^2-24x=ax(x+b)(x+c)
What are the missing values of a,b, and c
Answer:
a=3 b=-2 c=4
Step-by-step explanation:
Which equation can be used to solve for angle A?
sin (A)
2.4
sin (110°
4.6
sinca) = sin (1109
sin.ca - sin (1209
sin
sin (110
4.6
2.4
sin (A) - sin (110)
3.2
4.6
sin (A) - sin (1109)
4.6
3.2
C
By the law of sines, [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex] where A, B, C are the angles and a, b, c are the lengths of the sides opposite their respective angles. In this case, [tex]110^{\circ}[/tex] is opposite 4.6 and A is opposite 3.2, so [tex]\frac{sinA}{3.2}=\frac{sin(110^{\circ})}{4.6}[/tex], giving the answer.
Answer:
it’s c
Step-by-step explanation:
The quotient of three times a number and 4 is at least -16
Quotient is division,
Writing the equation out you get:
3x/4 ≥ -16
Now we can solve by x.
First multiply both sides by 4:
3x ≥ -64
Now divide both sides by 3:
x ≥ -64/3
what is the ratio of 8 to 8
Answer:
1 to 1
Step-by-step explanation:
8 to 8 = 8:8 = 8/8
You can treat a ratio as a fraction. Reduce the fraction 8/8 by dividing the numerator and denominator by 8.
8/8 = 1/1
8 to 8 = 1 to 1
Answer:
1:1
Step-by-step explanation:
A ratio says that "for every _ of this quantity, you have _ of another quantity". This is just saying for every 8 of one thing, you have 8 of another. And then you can simplify, just like a fraction.
47. If the sum of 2r and 2r + 3 is less than
11, which of the following is a possible
value of r?
(A) 11
(B) 10
(C) 3
(D) 2
(E) 1
Answer:
(E) 1
Step-by-step explanation:
2r+ (2r+3 ) < 11
Combine like terms
4r+3 < 11
Subtract 3 from each side
4r +3-3 < 11-3
4r < 8
Divide each side by 4
4r/4 < 8/4
r <2
The only possible choice is 1
Answer:
(E) 1
Step-by-step explanation:
the sum of 2r and 2r+3 less than 11 means :
2r+2r+3<11
we simplify we get :
4r+3<11
we take the 3 to the left :
4r<11-3
means
4r<8
we divide both sides by 4 we get :
r<2
so among all those values only the 1 satisfies the condition 1<2
so the answer is E
Classify the isometry.
a) glide reflection
b) reflection
c) rotation
d) translation
Answer:
A. glide reflection
Step-by-step explanation:
This is a glide reflection since the figure has been both reflected over a line and transported downwards.
Answer:
a) glide reflection
Step-by-step explanation:
An isometry is a transformation of a figure in the plane that preserves lenght, it could be reflections, rotations, or translations, in the figure you can se what is called a glide reflection, which is a reflection of the figure over a line, and then a translation of the same figure.
what is the solution of sqrt(x+2) -15=-3
Answer:
x = 142
Step-by-step explanation:
We are given the following expression for which we are to find the solution:
[tex] \sqrt { x + 2 } - 1 5 = - 3 [/tex]
Rearranging the equation to get:
[tex] \ sqrt { x + 2 } = - 3 + 1 5 [/tex]
Taking square root on both sides of the equation to get:
[tex](\sqrt{x+2} )^2=(12)^2[/tex]
[tex]x+2=144[/tex]
x = 142
[tex]\displaystyle\\\sqrt{x+2}-15=-3\\\\\sqrt{x+2}=-3+15\\\\\sqrt{x+2}=12~~\Big|~^2\\\\x+2=144\\\\x=144-2\\\\\boxed{x=142}[/tex]
.
Your friend has 100$ when he goes to the fair and 20$ on food. Rides at the fair cost $2 per ride. Which function can be used to determine how much he has left after X rides
Find three rational numbers between -2 and 1 ?
Answer:
-19/10,-18/10,-17/10
Step-by-step explanation:
multiply the both numbers up and down by 10.
then find the numbers
Answer:-1, 0, -1.33
Step-by-step explanation: Rational numbers include those with repeating decimals, natural, counting, etc.
what number should be added to both sides of the equation to complete the square
xsquared2-10x=7
Answer:
subtract 2 from each side and o think u decide the last two numbers
Answer:
Step-by-step explanation:2-10x=7
First you have to subtract you 2 on both sides so it would 7-2= 5
You are left with -10x =5
Then you divide your -10x by -10 to get rid of your x
Last you divide 5/-10
Which choice is the conjugate of the expression below when x>-4 5-square root of x+4
Answer:
[tex]5+\sqrt{x+4}[/tex]
Step-by-step explanation:
The conjugate of the radical expression [tex]a+\sqrt{b}[/tex] is [tex]a-\sqrt{b}[/tex]
The conjugate of the radical expression [tex]a-\sqrt{b}[/tex] is [tex]a+\sqrt{b}[/tex]
The sign of the radical becomes its additive inverse in the conjugate,
The given expression is
[tex]5-\sqrt{x+4}[/tex] where [tex]x>-4[/tex] (domain)
The conjugate of this expression is [tex]5+\sqrt{x+4}[/tex]
Answer:
The conjugate is 5+√x+4
Step-by-step explanation:
To find the conjugate of of expression 5-√x+4
when x>-4
First let us understand that in simple terms terms the conjugate of a radical simply involves the change in sign of the radical
in the problem the conjugate of
5-√x+4 is 5+√x+4
it is that simple Just alternate the sign and you are done!!!
What is .7995 rounded to the nearest cent?
Answer:
.7995 rounded to the nearest cent is 0.80 cents
Answer:
.7995 rounded to the nearest cent is .80.
Step-by-step explanation:
Rounding with numbers higher than 4 makes them round up, lower than 5 makes them round down.
What are the solutions of 3x^2 - x +7 =0?
Answer: Option A
[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function.
For a function of the form
[tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case the function is:
[tex]3x^2-x+7=0[/tex]
So
[tex]a=3\\b=-1\\c=7[/tex]
Then using the quadratic formula we have that:
[tex]x=\frac{-(-1)\±\sqrt{(-1)^2-4(3)(7)}}{2(3)}[/tex]
[tex]x=\frac{1\±\sqrt{1-84}}{6}[/tex]
[tex]x=\frac{1\±\sqrt{-83}}{6}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex]
[tex]x=\frac{1\±\sqrt{83}*\sqrt{-1}}{6}[/tex]
[tex]x=\frac{1\±\sqrt{83}i}{6}[/tex]
[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]
Final answer:
The solutions to the equation 3x² - x + 7 = 0 are complex numbers. Using the quadratic formula, we find the solutions to be x = (1 + i√83) / 6 and x = (1 - i√83) / 6.
Explanation:
The solutions of the quadratic equation 3x² - x + 7 = 0 cannot be real numbers because the discriminant (b² - 4ac), in this case, is negative ((-1)² - 4(3)(7) = 1 - 84 = -83). Therefore, we need to use the quadratic formula to find the complex solutions. This formula is given by x = (-b ± √(b² - 4ac)) / (2a). By substituting the values from the equation into the quadratic formula, we obtain the complex solutions.
Quadratic formula application:
x = (-(-1) ± √((-1)² - 4(3)(7))) / (2(3))
x = (1 ± √(-83)) / 6
Therefore, the two complex solutions are x = (1 + i√83) / 6 and x = (1 - i√83) / 6, where i is the imaginary unit.
To confirm these answers, we can substitute each value back into the original equation and verify by simplification that each results in an identity.