Answer:
[x + 3][2x² - 7]
Step-by-step explanation:
Start out by doing this: [2x³ + 6x² ] - [7x - 21]
↑ ⤻ ↑
GCF: 2x² GCF: -7
Do as so: 2x²[x + 3] -7[x + 3]
You see, one factor is already found [x + 3]. You only use it ONCE. Now, the other factor comes from your two Greatest Common Factors from both groups [2x² - 7]. Together, you end up with the above answer. That arrow under the negative tells you that it is attached to the 3 [distribution of the negative].
Well, I am joyous to assist you anytime.
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
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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:
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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
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
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
Two angles are said to be congruent if
Answer:
Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure.
Two angles are said to be congruent if they are equal. For example, if two triangles each have an angle of 42 degrees, then those angles are congruent.
Is the following relation a function?
{(3, −2), (1, 2), (−1, −4), (−1, 2)}
Answer:
It's not a function.Step-by-step explanation:
A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.
We have:
{(3, -2), (1, 2), (-1, -4), (-1, 2)}
for x = -1 are two values of y = -4 and y = 2. Therefore this realtion is not a function.
Answer: No, it is not a function.
Step-by-step explanation:
A function is a special kind of relation between two variables commonly x and y such that each x (input) value corresponds to a unique y(output) value.The given relation: {(3, −2), (1, 2), (−1, −4), (−1, 2)}
According to the above definition, the given relation is not a function because -1 corresponds to two different output values i.e. -4 and 2.
Hence, the given relation is not a function.
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]
.
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
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
A: What are the solutions to the quadratic equation x^2+9=0?
B: What is the factored form of the quadratic expression x^2+9?
Select one answer for question A, and select one answer for question B.
A: x=3
A: x=-3i
A: x=3i or x=-3i
A: x=3 or x=-3
B: (x+3)(x+3)
B: (x-3i)(x-3i)
B: (x+3i)(x-3i)
B: (x+3)(x-3)
Answer:
Part A)
x=-3i
x=3i
Part B)
(x+3i)(x-3i)
Step-by-step explanation:
Given:
Part A)
x^2+9=0
x^2=-9
x= √-9
x=√-1 *√9
x=± i *3
x=±3i
Part B)
x^2+9=0
x^2 - (-9)=0
x2-(3i)^2=0
(x-3i)(x+3i)=0 !
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.
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:
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I am equation of the line that passes through the point (2,3) with slope 3 please answer
[tex]\huge{\boxed{y-3=m(x-2)}}[/tex]
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a point on the line.
Substitute the values. [tex]\boxed{y-3=m(x-2)}[/tex]
Note: This is in point-slope form. Let me know if you need a different form. Also, if you have any more problems similar to this, I encourage you to try them on your own, and ask on here if you are having trouble.
Answer:
y-3 = 3(x-2) point slope form
y = 3x-3 slope intercept form
Step-by-step explanation:
We can use the point slope form of the equation for a line
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is the point
y-3 = 3(x-2) point slope form
If we want the line in slope intercept form
Distribute
y-3 = 3x-6
Add 3 to each side
y-3+3 = 3x-6+3
y = 3x-3 slope intercept form
Identify the least common multiple of x2 − 10x + 24 and x2 − x − 12.
Answer:
(x-4)(x-6)(x+3) or in more compressed form x³-7x²-6x+72
Step-by-step explanation:
To find the L.C.M, w first factorize each of the expressions.
x²-10x+24
Two numbers that when added give -10 but when multiplied give 24
will be, -4 and -6
Thus the expression becomes:
x²-4x-6x+24
x(x-4)-6(x-4)
=(x-4)(x-6)
Let us factorize the second expression.
x²-x-12
Two numbers when added give -1 and when multiplied give -12
are 3 and -4
Thus the expression becomes: x²-4x+3x-12
x(x-4)+3(x-4)
(x-4)(x+3)
Therefore the LCM between (x-4)(x-6) and (x-4)(x+3)
will be
(x-4)(x-6)(x+3)
We can multiply the expression as follows.
(x-4)(x-6)
x²-6x-4x+24 = x²-10x+24
(x+3)(x²-10x+24)
=x³-10x²+24x+3x²-30x+72
=x³-7x²+-6x+72
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]
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
Give 5 mathematical examples of additive inverse.
Answer:
−5 + 5 = 0
-6+6=0
14+-14=0
70+-70=0
100+-100=0
Step-by-step explanation:
hope this helps
Triangle ABC is to be dilated through point P with a scale factor of 3. How many units away from point A along ray PA will A’ be located?
Answer:
Point A' will be located 10 units away from point A along ray PA
Step-by-step explanation:
we have
The scale factor is 3
step 1
Find out the distance PA'
we know that
The distance PA' is equal to multiply the distance PA by the scale factor
so
[tex]PA'=PA*3[/tex]
we have
[tex]PA=5\ units[/tex]
substitute the given values
[tex]PA'=(5)*3=15\ units[/tex]
step 2
Find out how many units away from point A along ray PA will A’ be located
we know that
[tex]PA'=PA+AA'[/tex]
we have
[tex]PA=5\ units[/tex]
[tex]PA'=15\ units[/tex]
substitute the given values and solve for AA'
[tex]15=5+AA'[/tex]
[tex]AA'=15-5=10\ units[/tex]
therefore
Point A' will be located 10 units away from point A along ray PA
Answer:
10 units
Step-by-step explanation:
Let theta be an angle in quadrant II such that cos theta = -2/3
Find the exact values of csc theta and tan theta.
Answer:
So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].
Step-by-step explanation:
Ok so we are in quadrant 2, that means sine is positive while cosine is negative.
We are given [tex]\cos(\theta)=\frac{-2}{3}(\frac{\text{adjacent}}{\text{hypotenuse}})[/tex].
So to find the opposite we will just use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
[tex](2)^2+b^2=(3)^2[/tex]
[tex]4+b^2=9[/tex]
[tex]b^2=5[/tex]
[tex]b=\sqrt{5}[/tex] This is the opposite side.
Now to find [tex]\csc(\theta)[/tex] and [tex]\tan(\theta)[/tex].
[tex]\csc(\theta)=\frac{\text{hypotenuse}}{\text{opposite}}=\frac{3}{\sqrt{5}}[/tex].
Some teachers do not like the radical on bottom so we will rationalize the denominator by multiplying the numerator and denominator by sqrt(5).
So [tex]\csc(\theta)=\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}=\frac{3 \sqrt{5}}{5}[/tex].
And now [tex]\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt{5}}{-2}=\frac{-\sqrt{5}}{2}[/tex].
So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].
Answer:
[tex]tan\theta{3}=-\frac{\sqrt5}{2}[/tex]
[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]
Step-by-step explanation:
We are given that [tex]\theta[/tex] be an angle in quadrant II and [tex]cos\theta=-\frac{2}{3}[/tex]
We have to find the exact values of [tex]cosec\theta[/tex] and [tex]tan\theta[/tex].
[tex]sec\theta=\frac{1}{cos\theta}[/tex]
Then substitute the value of cos theta and we get
[tex]sec\theta=\frac{1}{-\frac{2}{3}}[/tex]
[tex]sec\theta=-\frac{3}{2}[/tex]
Now, [tex]1+tan^2\theta=sec^2\theta[/tex]
[tex]tan^2\theta=sec^2\theta-1[/tex]
Substitute the value of sec theta then we get
[tex]tan^2\theta= (-\frac{3}{2})^2-1[/tex]
[tex]tan^2\theta=\frac{9}{4}-1=\frac{9-4}{4}=\frac{5}{4}[/tex]
[tex]tan\theta=\sqrt{\frac{5}{4}}=-\frac{\sqrt5}{2}[/tex]
Because[tex] tan\theta [/tex] in quadrant II is negative.
[tex]sin^2\theta=1-cos^2\theta[/tex]
[tex]sin^2\theta=1-(\farc{-2}{3})^2[/tex]
[tex]sin^2\theta=1-\frac{4}{9}[/tex]
[tex]sin^2\theta=\frac{9-4}{9}=\frac{5}{9}[/tex]
[tex]sin\theta=\sqrt{\frac{5}{9}}[/tex]
[tex]sin\theta=\frac{\sqrt5}{3}[/tex]
Because in quadrant II [tex]sin\theta[/tex] is positive.
[tex]cosec\theta=\frac{1}{sin\theta}=\frac{1}{\frac{\sqrt5}{3}}[/tex]
[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]
[tex]cosec\theta[/tex] is positive in II quadrant.
write a linear equation in point slope form for the line that goes through (-1, 1) and (1, -3)
Answer:
y - 1 = -2(x + 1).
Step-by-step explanation:
The slope = (-3-1)/(1 - -1)
= -4 / 2
= -2.
In point slope form:
y - y1 = m(x - x1)
Using m = -2 and the point (-1, 1):
y - 1 = -2(x + 1).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (1, - 3)
m = [tex]\frac{-3-1}{1+1}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
Using either of the 2 points as a point on the line, then
Using (- 1, 1)
y - 1 = - 2(x - (- 1)), that is
y - 1 = - 2(x + 1) ← in point- slope form
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!!!
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
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
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:
What is the length of the unknown leg in the right triangle?
Answer:
a = 20 cm
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for a
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
a² + 21² = 29²
a² + 441 = 841 ( subtract 441 from both sides )
a² = 400 ( take the square root of both sides )
a = [tex]\sqrt{400}[/tex] = 20
A circle with a radius of 10 inches is placed inside a square with a side length of 20 inches. Find the area of the square.
a. 400
b. 413
c. 314
d. 143
Answer:
The correct answer is option a. 400
Step-by-step explanation:
Points to remember
Area of square = a²
Where 'a' is the side length of square
To find the area of square
It is given that, the side length of square is 20 inches.
Here a = 20 inches
Area = a²
= 20²
= 400
Therefore the correct answer is option a. 400
HELP ASAP AND GETS SOME POINTS AND BRAINLEST!!!!
Answer:
9x² + 28x - 32
Step-by-step explanation:
Given
(9x - 8)(x + 4)
Each term in the second factor is multiplied by each term in the first factor, that is
9x(x + 4) - 8(x + 4) ← distribute both parenthesis
= 9x² + 36x - 8x - 32 ← collect like terms
= 9x² + 28x - 32
Answer:
Option D
Step-by-step explanation:
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.