Answer:
[tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Step-by-step explanation:
Roots of quadratic equations [tex]ax^{2}+bx+c=0[/tex] calculated as:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
First, compare [tex]ax^{2}+bx+c=0[/tex] with [tex]x^{2}+2x-22=0[/tex]
here a = 1 , b = 2 and c = -22
Now, plug the value of a,b and c in [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x=\frac{-2\pm \sqrt{2^{2}-4(1)(-22)}}{2(1)}[/tex]
[tex]x=\frac{-2\pm \sqrt{4+88}}{2}[/tex]
[tex]x=\frac{-2\pm \sqrt{92}}{2}[/tex]
[tex]x=\frac{-2\pm 2\sqrt{23}}{2}[/tex]
[tex]x=-1\pm \sqrt{23}[/tex]
Hence, [tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile? 0.68 miles 0.81 miles 1.15 miles 1.44 miles
The total distance covered by her is 0.81 miles.
Given thatAlyssa is jogging near Central Park.
She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.
She then turns right again and runs along Broadway until she reaches her starting point.
We have to determine
How long is her total run to the nearest hundredth of a mile?
According to the question
She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.
Alyssa's route can be considered a right triangle with legs of length 0.19 and 0.28 (hundredths).
The total distance run is determined by using the Pythagoras theorem.
What is the Pythagorean theorem?Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Therefore,
The distance run by her is,
[tex]\rm x^2 = (0.19)^2 +(0.28)^2\\\\ x^2=0.0361 + 0.784\\ \\ x^2 = .1145\\ \\ x= \sqrt{.1145} \\\\ x= 0.34[/tex]
Therefore,
The total distance covered by her is,
= .34 + .19 + .28
= 0.81 miles
Hence, the total distance covered by her is 0.81 miles.
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The function f(x) = is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
Answer:
A
Step-by-step explanation:
The East Bay Deli, makes 6.85 pounds of pasta salad each day. West Bay Deli makes four times that amount each day. How many combined pounds of pasta salad is made per week between the two delis? Find a fourth of their combined weekly production of pasta salad.
what type of number can be written as a fraction where p and q are intergers and q is not equal to zero
A family has two cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. during one particular week, the two cars went a combined total of 675 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?
car 1 = x
car 2 = y
x+y =40 gallons
x=40-y
15x +20y = 675
15(40-y) +20y = 675
600-15y +20y =675
600+5y = 675
5y=75
y=75/5 = 15 gallons
x=40-15 =25 gallons
Car 1 used 25 gallons
Car 2 used 15 gallons
What is the length of the hypotenuse in the triangle below ?
What does it mean for an equation to have no solution or infinitely many solutions?
PLEASE GIVE ME A DETAILED RESPONSE AS IM TAKING MODULE 7 ALGEBRA DBA TOMORROW AT 7PM
No-Solution implies an inconsistent equation, while infinitely many solutions indicate a condition that holds true for any value of variable.
When an equation has No-Solution, it means that there is no value of variable that satisfies equation. In other words, equation represents an inconsistent condition, and solution set is empty. For example, equation 2x + 5 = 2x + 7 has no solution because the variable x cancels out, leaving an inconsistency (5 ≠ 7),
When an equation has infinitely many solutions, it means that any value of variable will satisfy equation. The equation represents a condition that is always true, regardless of chosen value.
For example, the equation x + 5 = x + 5 has infinitely many solutions because any value of x will make the equation true (such as x = 1, x = 2, x = 3, and so on).
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Part A: If (7 to the power of 2)x = 1, what is the value of x?
Part B: If (7to the power of 0)x = 1, what are the possible values of x?
Which of the following would best represent a cosine function with an amplitude of 3, a period of pi/2 , and a midline at y = –4? (1 point)
f(x) = –4 cos 4x + 3Answer:
D) f(x) 3 cos 4x-4 (I just took it)
Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be
Approximately 25,500 people
Approximately 24,8500 people
Approximately 25,150 people
If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.
Correct Answer:
p: The tire is flat. q: I will have to change it. p -> q
He number of years of education of self-employed individuals in the united states has a population mean of 13.6 years and a population standard deviation of 3.0 years. if we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the standard deviation of the sampling distribution of (the sample mean)
We can solve this problem by using the formula:
s = σ / sqrt(n)
where,
s = standard deviation of the sample
σ = standard deviation of the population = 3 years
n = number of samples = 100
Substituting:
s = 3 years / sqrt (100)
s = 0.3 years (ANSWER)
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
From the information given:
The measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:
[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]
[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]
[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]
[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]
Therefore, the measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
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Find the measure of an angle whose measure is 20° less than the measure of its supplement.
If Mercury's mass is 3 × 10^23 kilograms, and Saturn's mass is 6 × 10^26 kilograms, which statement is true?
Answer:
Saturn has about 2,000 times more mass.
Solve for x. A.x=7.5 B.x=16 C.x=17.5 D.x=27.5
What is the common difference of the following arithmetic sequence?
100, 102, 104, 106,…
The common difference in the arithmetic sequence 100, 102, 104, 106,... is 2.
Arithmetic Sequence: 100, 102, 104, 106,...
Common Difference: The common difference in an arithmetic sequence is the constant value by which each term is increased or decreased. In this sequence, the common difference is 2 because each term increases by 2.
Calculation: 102 - 100 = 2, 104 - 102 = 2, 106 - 104 = 2, so the common difference is 2.
Philip buys the pizza shown below: A circular pizza is shown. The center is labeled as point A and a point on the circumference is marked B. What does AB represent?
triangle pqr is a right triangle. If PQ = 8, what is PR?
The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. The length of the side PR in ΔPQR is 4√3 units.
What is the 30-60-90 right triangle?The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.
For the given right-angled triangle, we can use the 30-60-90 rule. The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.
Therefore, we can write,
PQ = 2(RQ)
8 = 2(RQ)
RQ = 4
PR = (RQ)√3
PR = 4√3
Hence, the length of the side PR in ΔPQR is 4√3 units.
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Help please.........,
y-6 = -4(x+1)
y-6 = -4x-4
add 6 to each side
y=-4x+2
A is the correct answer
What of the above terms indicates imaginary parallel lines that circle the earth?
If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.
A vertical stretch in the context of graphing functions occurs when the function is multiplied by a positive constant greater than 1, resulting in the graph being stretched vertically by that factor without affecting the y-intercept.
A vertical stretch occurs when we multiply the function by a positive constant greater than 1. For example, if we have y = a f(x) and a is greater than 1, this results in the graph being stretched vertically by a factor of a. This type of transformation doesn't affect the y-intercept since the behavior of the graph at x=0 remains unchanged. Multiplying the independent variable by a constant such as 1/2 would result in a horizontal stretching or compression, but this is different from the vertical stretching effect we are discussing here.
Additionally, suppose the vertical stretch factor is a natural number. In that case, we can think of the stretched function as being the sum of the original function added to itself repeatedly that number of times. This additive property also extends to the derivative, as the derivative of the vertically stretched function is the original derivative multiplied by the stretch factor. This is known as the vertical stretch property in the context of derivatives and calculus.
The screen aspect of a widescreen tv is 16.9. What are the width and height of a 32 inch tv? Round answer to the nearest tenth of an inch.
I need the blue one done! please help!!
No. Of roots in eq 8sec^x-6secx+1=0
Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3
Given expression: [tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}[/tex].
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x-3:\quad x\left(x-3\right)[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]
[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{4\left(x-3\right)}{x\left(x-3\right)}-\frac{x}{x\left(x-3\right)}[/tex]
[tex]=\frac{4\left(x-3\right)-x}{x\left(x-3\right)}[/tex]
[tex]=\frac{3x-12}{x\left(x-3\right)}[/tex]
[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{x}{x\left(x-3\right)}+\frac{4\left(x-3\right)}{x\left(x-3\right)}[/tex]
[tex]=\frac{x+4\left(x-3\right)}{x\left(x-3\right)}[/tex]
[tex]=\frac{5x-12}{x\left(x-3\right)}[/tex]
[tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}=\frac{\frac{5x-12}{x\left(x-3\right)}}{\frac{3x-12}{x\left(x-3\right)}}[/tex]
[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]=\frac{\left(5x-12\right)x\left(x-3\right)}{x\left(x-3\right)\left(3x-12\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]
[tex]=\frac{\left(5x-12\right)\left(x-3\right)}{\left(x-3\right)\left(3x-12\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]
[tex]=\frac{5x-12}{3x-12} \ \ \ : Final Answer.[/tex]
Susie is paying $558.16 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?
558.16 x 12 = 6697.92 every year
6697.92 x 30 = 200937.60 total
200937.60-150000 = $50,937.60 total interest paid
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is __________
The volume is _________
Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³
Step-by-step explanation:
2x – 4y = 12 3x – 6y = 21 solve
How many sides does a polygon have with an interior angle of 108?