Faith is 1/5 get morthers age. their combined ages are 30. how old is faith
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A smart phone costs $149.99 before tax. The tax on the smart phone is 7%.
What is the total cost of the smart phone?
Round your answer to the nearest cent.
Answer/Step-by-step explanation:
149.99+(149.99*0.07)=160.4893. Round to $160.49
30inches increased by 30 percent
Which statement correctly describes a kite
What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
The solution to the system of equations are ±2i and ±i
Quartic equationsGiven the quartic equation
x^4 + 3x^2 + 2 = 0
Let u = x^2 to have:
(x^2)^2 + 3x^2 + 2 = 0
u^2 + 3u + 2 = 0
Factorize
u^2 + u +2u + 2 = 0
u(u + 1) + 2(u + 1) = 0
(u + 2)(u + 1) = 0
u = -2 or -1
If u = x^2
-2 = x^2
x = √-2
x = 2i
Similarly
If u = x^2
-1 = x^2
x = √-1
x = i
Hence the solution to the system of equations are ±2i and ±i
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Final answer:
To solve the equation x^4 + 3x^2 + 2 = 0 using u substitution, substitute x^2 for u and solve the quadratic equation. The resulting solutions in the complex number system are x = i, -i, √2i, and -√2i. There are no real solutions for this equation.
Explanation:
The solutions of the equation x4 + 3x2 + 2 = 0 can be found using u substitution. First, let's substitute u for x2, which transforms the original equation into the form u2 + 3u + 2 = 0. This is a quadratic equation, and we can solve it using the quadratic formula or by factoring. Factoring (u + 1)(u + 2) = 0, we get the solutions for u as u = -1 and u = -2. Since u is a substitute for x2, we then solve for x.
For u = -1, the equation x2 = -1 has no real solutions because the square of a real number cannot be negative. However, in the complex number system, the solutions are x = i and x = -i, where i is the square root of -1.
For u = -2, the equation x2 = -2 also has no real solutions, but the complex solutions are x = √2i and x = -√2i.
Therefore, the full set of solutions for the original equation are x = i, -i, √2i, and -√2i.
This table shows the input and output values for an exponential function f(x)
What are the ratios of outputs for any two inputs that are 1 apart?
A. 1/2
B. 4
C. 1/8
D. 2
x −3, −2, −1, 0, 1, 2, 3
f(x) 1/256, 1/64, 1/16, 1/4, 1, 4, 16
Answer:
B. 4
Step-by-step explanation:
This table that shows the input and output values for an exponential function f(x) is,
x -3 -2 -1 0 1 2 3
f(x) 1/256 1/64 1/16 1/4 1 4 16
Taking [tex]x=2[/tex] and [tex]x=3[/tex] as input (because they are 1 apart), the ratio of output is,
[tex]=\dfrac{f(3)}{f(2)}[/tex]
[tex]=\dfrac{16}{4}[/tex]
[tex]=4[/tex]
Answer:
The correct answer is B. 4
Step-by-step explanation:
State the y-coordinate of the y-intercept for the function below.
ƒ(x)=x^3-x^2-x+1 ...?
Answer:
1
Step-by-step explanation:
Answer is 1 for Apex Precal
Which of the following statements is true?
A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
A movie theater charges $11 for each adult and $6 for each ticket. one day, they sold 163 tickets and made $1578. How many of each ticket did they sell?
The movie theater sold 117 adult tickets and 46 child tickets.
Explanation:To solve this problem, we can set up a system of equations. Let's say the number of adult tickets sold is x and the number of child tickets sold is y. We can then write two equations based on the given information:
x + y = 163 (equation 1, representing the total number of tickets sold)11x + 6y = 1578 (equation 2, representing the total amount earned)We can solve this system of equations by either substitution or elimination. Let's use elimination:
Multiply equation 1 by 6 to make the coefficients of y in both equations equal:6x + 6y = 978
Subtract equation 1 from equation 2 to eliminate y:(6x + 6y) - (11x + 6y) = 978 - 163
-5x = -585
Divide by -5:
x = 117
Substitute x back into equation 1 to find y:117 + y = 163
y = 163 - 117
y = 46
Therefore, 117 adult tickets and 46 child tickets were sold.
What is the exact circumference of the circle?
A. 10π feet
B. 20π feet
C. 40π feet
D. 60π feet
circumference of a circle= pi multiplied by the diameter
= 20ft x pi
=20 pi feet so the answer is b
According to the Wall Street Journal, 14,200,000 videotape copies of Walt Disney's Fantasia have
been sold to date. Write that number in scientific notation.
A. 1.42 × 10^7
B. 1.42 × 10^6
C. 142 × 1,000,000
D. 142 × 10^7
scores on a test are normally distributed with a mean fo 69.2 and a standard deviation of 9.4, find p81
What is 3/4 x 2/3 in simplest form?
p and q are prime numbers. p3 x q = 56. Find p and q.
A parallelogram has a base that measures 5 units and a height that measures (x + 6) units. The area of this parallelogram is 20 square units. What must be the value of x?
Choose one answer.
a. x=4
b. x=-2
c. x=5
d. x=15
To solve for 'x' in the parallelogram area equation, we multiplied the given base (5 units) by the height (x + 6 units) and set it equal to the given area (20 square units). After simplifying, we found that x must be -2 to satisfy the equation 5x + 30 = 20.
Explanation:The question presented is a typical algebra problem where we need to find the value of 'x' in the context of the area of a parallelogram. The base of the parallelogram is given as 5 units and its height is given as (x + 6) units, with the total area given as 20 square units. Since the formula for the area of a parallelogram is base × height, we can set up the equation 5 × (x + 6) = 20 to find the value of x.
Now, we will solve for x:
Multiply the base by the height: 5(x + 6) = 20.Distribute the 5: 5x + 30 = 20.Subtract 30 from both sides to solve for x: 5x = -10.Divide both sides by 5 to find x: x = -2.Hence, the correct answer is b. x=-2.
What are the factor pairs of 23?
Solve each compound inequality. Graph the solution
Help explain step by step
4x<=12and-7x<=21
All real numbers that are less then -3 or greater then or equal to 5
Use the diagram below to answer the following questions.
The value of x is
The measure of 1 is
The measure of 2 is
The measure of 3 is
The measure of 4 is
The measure of 5 is
The measure of 6 is
The measure of 7 is
The measure of 8 is
Answer:
The value of x is 24. The measures of angles 1,2,3,4,5,6,7,8 are 101, 79, 101, 101, 79, 79, 89, 89 respectively.
Step-by-step explanation:
If two line intersect each other, then vertical opposite angles are same.
[tex]3x+19=5x-29[/tex] (Vertical opposite angles)
[tex]19+29=5x-3x[/tex]
[tex]48=2x[/tex]
Divide both sides by 2.
[tex]24=x[/tex]
The value of x is 24.
Measure of angle 2 is
[tex]\angle 2 =3x+7=3(24)+7=79[/tex] (Vertical opposite angles)
The measure of angle 2 is 79°.
Measure of angle 1 is
[tex]\angle 1 =180-\angle 2=180-79=101[/tex] (Angle 1 and 2 are supplementary angles)
The measure of angle 1 is 101°.
Measure of angle 3 is
[tex]\angle 3 =180-\angle 2=180-79=101[/tex] (Angle 3 and 2 are supplementary angles)
The measure of angle 3 is 101°.
Measure of angle 4 is
[tex]\angle 4 =4x+5=4(24)+5=101[/tex] (Vertical opposite angles)
The measure of angle 4 is 101°.
Measure of angle 5 is
[tex]\angle 5 =\angle 2=79[/tex] (Alternate Interior Angles)
The measure of angle 5 is 79°.
Measure of angle 6 is
[tex]\angle 5 =\angle 6=79[/tex] (Vertical opposite angles)
The measure of angle 6 is 79°.
Measure of angle 7 is
[tex]\angle 7 =180-(5x-29)=180-(5(24)-29)=89[/tex] (Supplementary angles)
The measure of angle 7 is 89°.
Measure of angle 8 is
[tex]\angle 8 =\angle 7=89[/tex] (Vertical opposite angles)
The measure of angle 8 is 89°.
Mary baked 21 cookies on saturday and twice that many on sunday for a school fundraiser. 4 cookies fell on the ground and had to be thrown out. if she packaged 3 cookies to a bag, how many cookies were left over?
Solve the problem.
Find all values of k so that the given points are\sqrt {29} units apart. (-5, 5), (k, 0)
Choose the right answer
a. 3, 7
b. 7
c. -3, -7
d. -7 ...?
Final answer:
The values of k that ensure the points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex]units apart are -3 and -7, derived using the Pythagorean theorem and algebraic manipulation.
Explanation:
To find all values of k so that the points (-5, 5) and (k, 0) are \(\sqrt{29}\) units apart, we use the distance formula derived from Pythagoras’ theorem, which is[tex]d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]. Here, [tex]\(x_1 = -5\), \(y_1 = 5\), \(x_2 = k\), and \(y_2 = 0\). Substituting the given values, we get:[/tex]
[tex]\(\sqrt{29} = \sqrt{(k + 5)^2 + (0 - 5)^2}\)[/tex]
Squaring both sides to eliminate the square root gives:
[tex]29 = (k + 5)^2 + 25[/tex]
Subtracting 25 from both sides, we get:
[tex]4 = (k + 5)^2[/tex]
Therefore, \(k + 5 = \pm2\), which simplifies to:
[tex]\(k + 5 = 2\) giving \(k = -3\)[/tex]
[tex]\(k + 5 = -2\) giving \(k = -7\)[/tex]
The values of k are -3 and -7, so the correct option is c. -3, -7.
The correct answer is option (c) -3, -7.
How is it so?
To find the values of k such that the given points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex] units apart, use the distance formula between two points in a plane:
[tex]\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given that the distance between the points is [tex]\(\sqrt{29}\)[/tex], we have:
[tex]\[ \sqrt{(k - (-5))^2 + (0 - 5)^2} = \sqrt{29} \][/tex]
[tex]\[ \sqrt{(k + 5)^2 + 5^2} = \sqrt{29}[/tex]]
[tex]\[ \sqrt{k^2 + 10k + 25 + 25} = \sqrt{29} \][/tex]
[tex]\[ \sqrt{k^2 + 10k + 50} = \sqrt{29} \][/tex]
Squaring both sides to eliminate the square root:
[tex]\[ k^2 + 10k + 50 = 29 \][/tex]
[tex]\[ k^2 + 10k + 21 = 0 \][/tex]
Solve this quadratic equation
[tex]\[ k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where a = 1, b = 10, and c = 21.
[tex]\[ k = \frac{-10 \pm \sqrt{10^2 - 4 \cdot 1 \cdot 21}}{2 \cdot 1} \][/tex]
[tex]\[ k = \frac{-10 \pm \sqrt{100 - 84}}{2} \][/tex]
[tex]\[ k = \frac{-10 \pm \sqrt{16}}{2} \][/tex]
[tex]\[ k = \frac{-10 \pm 4}{2} \][/tex]
[tex]\[ k = \frac{-10 + 4}{2} \] or \( k = \frac{-10 - 4}{2} \)[/tex]
[tex]\[ k = \frac{-6}{2} \] or \( k = \frac{-14}{2} \)[/tex]
[tex]\[ k = -3 \] \:or \( k = -7 \)[/tex]
So, the correct answer is option (c) -3, -7.
What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible.
A) 2the square root of 2.
B) 12the square root of 2.
C) 2the square root of 5.
D) 12the square root of 5.
Answer:
[tex]2\sqrt{5}[/tex]
C is the correct option.
Step-by-step explanation:
The given expression is [tex]\sqrt{180}-\sqrt{125}+\sqrt{5}[/tex]
In order to simplify the expression, we find the factors.
180 =6 ×6×5
125 = 5 ×5×5
Hence, we can rewrite the expression as
[tex]\sqrt{6\times6\times5}-\sqrt{5\times5\times5}+\sqrt{5}[/tex]
We can further write this expression as
[tex]\sqrt{6^2\times5}-\sqrt{5^2\times5}+\sqrt{5}[/tex]
Now, we can use the rule [tex]\sqrt{x^2}=x[/tex]
[tex]6\sqrt{5}-5\sqrt{5}+\sqrt{5}[/tex]
Finally, we can combine these like terms
[tex]2\sqrt{5}[/tex]
Hence, C is the correct option.
Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC. (See figure.)
The [tex]x[/tex] coordinates of the point A is [tex]\boxed{\bf 0}[/tex].
The [tex]x[/tex] coordinates of the point B is [tex]\boxed{\bf 0}[/tex].
The [tex]x[/tex] coordinates of the point C is [tex]\boxed{\bf 10}[/tex].
Further explanation:
Given:
The coin labeled as A lies on the [tex]y[/tex]-axis.
The coin labeled as B lies on the origin.
The coin labeled as C lies on the [tex]x[/tex]-axis.
The distance of the point B and C is [tex]10\text{ cm}[/tex].
Concept used:
The point which lies on the [tex]x[/tex]-axis, the value of its [tex]y[/tex]-coordinate is [tex]0[/tex].
The point which lies on the [tex]y[/tex]-axis, their [tex]x[/tex]-coordinate is [tex]0[/tex].
The coordinate of the origin is [tex](0,0)[/tex].
Calculation:
The coin labeled as A lies on the [tex]y[/tex]-axis therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].
The coin labeled as B lies on the origin therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].
The distance from point B to the point C is [tex]10\text{ cm}[/tex] and the coin labeled as C lies on the x axis it means that the [tex]x[/tex]-coordinate of the point is [tex]10[/tex].
Therefore, the [tex]x[/tex] coordinate of the point A is [tex]0[/tex].
The [tex]x[/tex] coordinate of the point B is [tex]0[/tex].
The [tex]x[/tex] coordinate of the point C is [tex]10[/tex].
Learn more:
1. Coordinate of the point : https://brainly.com/question/1286775
2. Equation: https://brainly.com/question/1473992
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Coordinate geometry, x-axis, y-axis, x-coordinate, y-coordinate, coin, square, three corners, three identical coins.
How many miles is it from honolulu to turtle bay?
The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.
Explanation:The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.
It's important to note that the actual distance traveled may vary depending on the specific route taken and any detours or alternate paths chosen.
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The equation x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b?
Answer:
The value of a+b is 1.
Step-by-step explanation:
The given equation is
[tex]x^2-1x-90=0[/tex]
It is given that this equation has two solutions {a,b}.
First of all find the factors of given equation. The middle term can be written as -10x+9x.
[tex]x^2-10x+9x-90=0[/tex]
[tex](x^2-10x)+(9x-90)=0[/tex]
Taking out common from each parenthesis.
[tex]x(x-10)+9(x-10)=0[/tex]
[tex](x-10)(x+9)=0[/tex]
Using zero product property, we get
[tex]x-10=0\Rightarrow x=10[/tex]
[tex]x+9=0\Rightarrow x=-9[/tex]
The value of a is 10 and b is -9. The sum of both the solutions is
[tex]a+b=10-9=1[/tex]
Therefore the value of a+b is 1.
I don't really know how to do this and I have to explain to my class how I got my answer. Help me!!!
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the distance in 4 h. Car A traveled 22 mph faster than Car B.
How fast did Car A travel?
_____mph
Find the range of y = 3cos4x - 2. -5 ≤ y ≤ 5 -5 ≤ y ≤ 1 -3 ≤ y ≤ 3 1 ≤ y ≤ 3
Answer:
{y|−5≤y≤1}
Step-by-step explanation:
The range of the function is y ∈ [-5, 1] or -5 ≤ y ≤ 1 if the function is y = 3cos4x - 2 option second is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
y = 3cos4x - 2
As we know, cosx ∈ [-1, 1]
-1 ≤ cosx ≤ 1
-1 ≤ cos4x ≤ 1
-3 ≤ 3cos4x ≤ 3
-5 ≤ 3cos4x - 2 ≤ 1
-5 ≤ y ≤ 1
Thus, the range of the function is y ∈ [-5, 1] or -5 ≤ y ≤ 1 if the function is y = 3cos4x - 2 option second is correct.
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PLEASE HELP!
A 20in. by 24in. photo is reduced so that the length (the longer dimension) is 15in.
What is the width of the reduced photo?
A: 11in
B: 12.5 in
C: 13.5 in
D: 18in
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Dimensions of the photo is given by
[tex]20\ in.\ by\ 24\ in.[/tex]
According to question, the photo is reduced so that the longer dimension is 15 inch.
So, Let the width of the reduced photo be x.
So, it becomes,
[tex]\frac{20}{x}=\frac{24}{15}\\\\x=\frac{15\times 20}{24}\\\\x=12.5\ in.[/tex]
So, the width of the reduced photo is 12.5 inch.
Hence, Option 'B' is correct.
which of the following is the correct factorization of the polynomial below?
27x^3+64
a) (3x+4)(9x^2-12x+16)
b) (9x+8)(3x^2-16x+8)
c) (3x^2+8)(9x-16x+8)
d) the polynomial is irreducible
...?
Answer:
a) (3x+4)(9x^2-12x+16)
Step-by-step explanation: