X+y=13and x-y=2 what is the value of x^2-y^2
Solve the inequality. Graph the solution set. 26+6b (>=) 2(3b+4 A. All real numbers b. b> or less than 1/2 c. no solutions
If the average price of four pairs of shoes is $50, and three of those pairs of shoes are priced at $35, $40 and $55, what is the price of the fourth pair of shoes?
Joe and Mary each pay the same price for a T-shirt. Before they buy it, Mary has $\$ 2$ more than Joe. To buy the T-shirt, Joe spends $ \$1 $ less than $\frac{2}{5}$ of his money, and Mary spends $\frac{1}{3}$ of her money. What was the total amount of money Joe and Mary originally had altogether?
Answer:
52
Step-by-step explanation:
Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.
Look at the figure. What is the next step in this construction of a line parallel to AC passing through point B.
A. use a protractor to measure ∠BAC
B. Draw a line through point B that intersects arc 2.
C. Measure the distance between AB and AC along arc 1 with a ruler.
D. Measure the distance between AB and AC along arc 1 with a compass.
Answer:
Option A is correct
Step-by-step explanation:
In the given figure to draw the parallel line to AC passing through B we have to tell the next step.
As lines AC and AB given and we know if lines are parallel then alternate angles are equal.
Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.
∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.
Hence, Option A is correct.
Use the drop-down menus to complete each statement to show why √21 is between 4 and 5.
Answer:
To show: [tex]\sqrt{21}[/tex] is between 4 and 5
We know:
21 is lies between two consecutive integer i.e, 16 and 25
We can write this as:
[tex]16 < 21 < 25[/tex]
or
[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]
Simplify:
[tex]4 < \sqrt{21} < 5[/tex]
⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.
Therefore, [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.
Answer:
We know that
[tex]16<21<25[/tex]
Because, 16 is less than 21 and 25 is more than 21.
Now, if we apply a square root to each part, we would have
[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]
Then, we solve each square root, except the square root of 21, because it doesn't have an exact result
[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]
So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.
In a random sample of 2121 people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a t-distribution to construct a 8080% confidence interval for the population mean muμ. what is the margin of error of muμ? interpret the results.
The margin of error can be calculated using the t statistic. The formula for margin of error is given as:
Margin of error = t * s / sqrt (n) ---> 1
Where,
t = the t score based on the given confidence level and degrees of freedom
n = number of samples = 21
s = standard deviation = 7.1
Degrees of freedom = n – 1 = 21 – 1 = 20
Based on the standard probability tables for t, the t score is:
t = 0.860
Substituting into equation 1:
margin of error = 0.860 * 7.1 / sqrt (21)
margin of error = 1.33
The range is:
range = 30.1 ± 1.33
range = 28.77, 31.43
Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.
I NEED THIS ASAP Are two regular hexagons always congruent? Explain your answer
The roots of the equation are 3 + 8i and 3 – 8i.
What is the value of c?
x2 – 6x + c = 0
c = [1]
How many hours are in 2 weeks?
At 2:00 Tony rented a mountain bike from the slick rock cyclery. He returned the bike at 5:00 after cycling 18 mi.Tony paid 24 for the rental. Find the rental rate in dollars per mile. Take the number of dollars and divide by the number rate mile
Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 – 25?
(x – 5)(x – 5)
(x + 5)(x + 5)
(x – 20)(x + 5)
(x – 5)(x + 5)
Answer:
its D
Step-by-step explanation:
For her phone service, Kala pays a monthly fee of $13 , and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $63.15 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
Regression and modeling with functions
HELP! What is the volume of the regular pyramid below????
Evaluate | 4t+n | if t=-2 and n=5
Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 123 c = 207
Kenji buys 3 yard of fabric for 7.47 then he relizes that he need 2 more yard how much fbric will he need
How do scientists communicate the results of investigations? A. by publishing articles in scientific journals B. by giving talks at scientific conferences C. by exchanging e-mails D. all of the above
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 200 pounds requires 250 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?
Which of the following is a simpler form of the expression sin (theta)sec(theta)÷ cos(theta)tan(theta)
Answer: [tex]sec \theta[/tex].
Step-by-step explanation: Given expression : [tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex]
We know,
[tex]sec \theta = \frac{1}{cos \theta}[/tex]
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
Substituting those values in given expression, we get
[tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex] =[tex]\frac{sin \theta\ \frac{1}{cos \theta} } {cos \theta\ \frac{sin \theta}{cos \theta} }[/tex]
= [tex]\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}[/tex]
Crossing out [tex]sin \theta \ cos \theta[/tex] from top and bottom, we get
=[tex]\frac{1}{cos \theta }[/tex]
= [tex]sec \theta[/tex].
Answer:
The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is [tex]\sec\theta[/tex]
Step-by-step explanation:
Given: Expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]
We have to writ the given expression in simplified form.
Consider , The given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]
Since, we know,
[tex]\sec\theta=\frac{1}{\cos\theta}[/tex]
and [tex]\tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]
Substitute, we have,
[tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}=\frac{\sin\theta \cdot\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{\sin\theta}{\cos\theta} }[/tex]
Simplify, we have,
[tex]=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }[/tex]
Simplify further, we get,
[tex]=\frac{1}{\cos\theta}=\sec\theta[/tex]
Thus, The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is [tex]\sec\theta[/tex]
Give the number of significant figures in this number 34.20
To take a taxi, it costs $3.00 point plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi, which includes the $1 tip you left. How many miles did you travel?
In triangle KLM LM = 7 and angle k equals 45 Find KL.
In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.
Explanation:In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.
Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.
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For what values of x is the rational expression below undefined?
Check all that apply.
x-4/3x^2-75
A. -3
B. -4
C. 3
D. -5
E. 4
F. 5
What are all the possible 3 digit number combinations 0-9?
Please Help!! Find the measure of angle 2. Image Attached
opposite angles have to equal 180
so 180-111 = 69
angle 2 is 69 degrees
A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...
A principal of $2600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 8 years?
Your computer monitor has a width of 13.93 inches and a height of 10.45 inches. what is the area of the monitor display in square meters
The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.
Explanation:To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.
Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.
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