we have
5/x=15/24
solve for x
Multiply in cross
15*x=24*5
x=24*5/15
x=8
answer is 8Find the domain and the range help please.
Answer:
Domain: [tex]-5 < x\leq 6[/tex]
Range: [tex]-5 < y\leq 2[/tex] and [tex]y=3[/tex]
Step-by-step explanation:
The domain does not include negative five because it is an open dot at (-5,-5)
The domain includes -2 even though their is an open dot because their is one closed dot at (-2, -2) as well.
The domain includes 3 because there is a closed dot at point (3,2)
The range does not include negative five because it is an open dot at (-5,-5).
Range does not include anything between [tex]2\leq x\leq 3[/tex] because there is nothing there.
Finally we include y=3 because the is a horizontal line where y=3.
PLEASE HELP ME!! The 7th grade has already saved $60 for a field trip to Hershey Park. They need to raise at least$720 in order to pay for the trip. They decide to sell T-shirts to raise money. They earn $12toward the trip for every T-shirt they sell.Write the inequality that represents this situationHow many T-shirts must they sell to eam at least $720? Show how you determined your answer
We have to calculate how many T-shirts the hay to sell in order to raise $720, including the $60 dollars they already saved.
They earn $12 for every T-shirt, so the amount of money raised is 12x, being x the number of T-shirts.
Then, 12x has to be at least equal to 720-60=660:
[tex]12x\ge660[/tex]Then, if we divide both sides by 12, we get the number of T-shirts they have to sell:
[tex]\begin{gathered} 12x\ge660 \\ \frac{12}{12}x\ge\frac{660}{12} \\ x\ge55 \end{gathered}[/tex]They have to sell at least 55 T-shirts.
The length of a rectangle is 3 centimeters longer than the width. The perimeter of the rectangle is less than 15cm. Figure out the inequality and solve.
we have the following:
[tex]\begin{gathered} l=3+w \\ 15>2\cdot l+2\cdot w \\ 15>2\cdot(3+w)+2\cdot w \\ 15>6+2w+2w \\ 15-6>4w \\ 4w<9 \\ w<\frac{9}{4} \end{gathered}[/tex]therfore, the answer is:
[tex]\begin{gathered} l=3+\frac{9}{4}=5.25 \\ w<\frac{9}{4}<2.25 \end{gathered}[/tex]Simplify the following 4^9x 4^3
Answer:
261144^x and 64
Step-by-step explanation:
4^9x = (4^9)^x = 262144^x
4^3 = 64
But maybe I don't understand the task?
Sandy takes a random sample of 10 of her classmates and determines their average height. She takes a second random sample of 10 OA. researcher error B. biased sampling OC. random sampling variation D. sampling error
Solution
Definition: Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
Answer
C. random sampling
What is the volume of a sphere with a radius of 6.891 cm?
Given: A sphere with a radius of 6.891 cm.
Required: To determine the volume of the sphere.
Explanation: The volume of a sphere with radius r is given by the formula-
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting the value into the formula as-
[tex]V=\frac{4}{3}\times3.14\times(6.891)^3[/tex]Further solving gives the volume as-
[tex]V=1369.9828\text{ }cm^3[/tex]Final Answer: The volume of the sphere is 1369.983 cubic centimeters (approx).
Based on the picture..Find the area in terms of xFind the perimeter in terms of x
The area of a rectangle is given by the product of its dimensions.
If this rectangle has a length of 2x + 7 and a width of x + 4, its area is:
[tex]\begin{gathered} \text{Area}=\text{length}\cdot\text{width} \\ \text{Area}=(2x+7)(x+4)_{} \\ \text{Area}=2x^2+8x+7x+28 \\ \text{Area}=2x^2+15x+28 \end{gathered}[/tex]The perimeter is the sum of all side lengths, so we have:
[tex]\begin{gathered} \text{Perimeter}=(2x+7)+(x+4)+(2x+7)+(x+4) \\ \text{Perimeter}=6x+22 \end{gathered}[/tex]When a transversal crosses parallel lines, the alternate interior angles are ___?
From the illustration above, two parallel lines are crossed by a transversal. The marked angles are called alternate interior angles.
Alternate interior angles are congruent
When two coins are tossed at the same time, what is the theoretical probability of an outcome of one head and one tail?1/21/33/41/4
To find the proability we need to remember the product rule of proabbility that states that:
[tex]P(A\cap B)=P(A)P(B)[/tex]in this case event A is "getting head" and event B is "getting tail"; we know that each of this events have a proability of 1/2, then:
[tex]P(A\cap B)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore the probability we are looking for is 1/4.
Two angles in a triangle measures 101° and 29° what is the measure of the third angle?
We are given that two angles in a triangle measure 101° and 29°
What is the measure of the third angle?
Recall that the sum of three interior angles of a triangle must be equal to 180°
Let x be the third angle of the triangle, then we can write
[tex]x+101\degree+29\degree=180\degree[/tex]Let us solve the above equation for x
[tex]\begin{gathered} x+101\degree+29\degree=180\degree \\ x+130\degree=180\degree \\ x=180\degree-130\degree \\ x=50\degree \end{gathered}[/tex]Therefore, the measure of the third angle is 50°
Determine whether the following problem involves a permutation or combination. (It is not necessary to solve the problem.)How many different 2-letter passwords can be formed from the letters H, I, J, K, L, M, and N if no repetition of letters is allowed?
A permutation is an arrangement of outcomes in which the order does matter.
A combination is an arrangement of outcomes in which the order does not matter.
In this case, for example, the password HI is different from the password IH. In both cases, the outcomes (letters H and I) are the same, but the order of them changes the arrangement (the password). Therefore, the problem involves a permutation because the order of letters selected does matter
I need to know the answer to this question please
Given the equation:
[tex]-(-2+11)=2+(-11)[/tex]Let's identify the property demonstrated in the given equation.
The property demonstrated here is the distributive property.
To simplify the left side, we are to distribute the - sign to the terns in the parentheses using distributive property.
We have:
[tex]\begin{gathered} -(-2)+(-11) \\ \\ =2+(-11) \end{gathered}[/tex]Therefore, the property demonstrated here is the distributive property.
ANSWER:
Distributive property.
The exchange rate between Mexican pesos and U.S. dollars is 12. 54 pesos to 1dollar. If Chris travels to Mexico and converts $750 to pesos for spending money,how many pesos will he have? Round your answer to the nearest peso.
12.54 mexican pesos = 1 dollar
750 dollars x (12.54) = 9405 mexican pesos
Question 1 ask the same thing but only they ask if the account is growing or decaying and it was growing so nowQuestion 2 what is the rate of growth or decayA 250B 0.97C 0.03D 1.03
.Explanation
The question gives us an exponential equation and asked that we determine the growth rate
Growth rates refer to the percentage change of a specific variable within a specific time period
From the given expression:
[tex]f\mleft(x\mright)=250\left(1.03\right)^x[/tex]If we are to deduce the growth rate, then we will have to compare it with the general formula
[tex]\begin{gathered} f\lparen x)=A\left(b\right)^x \\ where\text{ b is the growth factor} \end{gathered}[/tex]The growth factor is the factor by which a quantity multiplies itself over time. The growth rate is the addend by which a quantity increases (or decreases) over time
Thus, in our case
[tex]\begin{gathered} Growth\text{ factor=b=1.03} \\ Growth\text{ rate =Growth factor -1} \end{gathered}[/tex]Thus
[tex]Growth\text{rate=Growthfactor-1=1.03-1=0.03}[/tex]Hence, the growth rate is 0.03
Because the account increases by 0.03 overtime
The answer is 0.03
MODELING WITH MATHEMATICS The top of theslide is 12 feet from the ground and has an angle ofdepression of 53°. What is the length of the slide?(See Example 6.)53%12 ft37. MULTIPLE REPRESENTATIONS You are standing ona cliff above an ocean. You see a sailboat from yourvantage point 30 feet above the ocean.a. Draw and label a diagram of the situation.b. Make a table showing the angle of depression andthe length of your line of sight. Use the angles 40°,50°, 60°, 70°, and 80°.c. Graph the values you found in part (b), with theangle measures on the x-axis.d. Predict the length of the line of sight when theangle of depression is 30°.
Given:
The height of the slide from the ground = 12 feet
The angle of depression = 53 degrees
Required:
Find the length of the slide.
Explanation:
The given triangle is the right triangle.
adjacent = 12 ft
we have to find the hypotenuse side.
Let the length of the slide is h ft.
Use the following trigonometric ratio:
[tex]cos\theta=\frac{adj.}{hyp.}[/tex][tex]\begin{gathered} cos53\degree=\frac{12}{h} \\ h=\frac{12}{cos53\degree} \\ h=\frac{12}{0.6018} \\ h=19.94 \\ h\approx20\text{ feet} \end{gathered}[/tex]Final Answer:
The length of the slide is approximately 20 ft.
Express twelve thousandths as a decimal.
twelve thousandths means 12 divided by a thousand. That is:
12/1000 = 0.012
so the 2 is in the column of the thousandths, and the 1 in the column of the hundredths.
Convert the rectangular coordinate, (-472, -4/2),to a polar coordinate (r, 0).r=[ Select]A= [Select ]
We have two formulas to convert from polar to cartesian coordinates:
x = r cos θ
y = r sin θ
We need to find the values of r and θ, in terms of x = -4 √2 and y = -4 √2
If we divide:
y/x = sin θ / cos θ = tan θ
Replacing x and y we find that:
tan θ = ( -4 √2 ) / ( -4 √2 ) = 1
We can calculate the inverse of the tan function:
θ = arc tan (1) = 225º,
Sorry, but the inverse of the tan function has many results. We can see that the results are two, 45º and also 45º+180º = 225º. The first one give us a point in the first quadrant (positive values for x and y); and the second one give us a point in the third quadrant (negative values for x and y). So we must select the second value in order to have negative values of x and y.
Now we must calculate the value of r. In order to calculate the value of r we can use the following formula:
[tex]x^2+y^2\text{ = r}^2[/tex]So, the value of r is (if we replace the values of x and y and compute the square root):
[tex]r\text{ = }\sqrt[]{x^2+y^2}\text{ = }\sqrt[]{64}=\text{ 8}[/tex]So the answer is:
r = 8
θ = 225º
Michaela has $2.05 in dimes and nickels in her change purse. She has seven more dimes than nickels. How many coins of each type does she have?
Answer: Michaela has 16 Dimes, and 9 Nickels.
3. Eric has rock and classical mp3 on his computer. The number of rock mp3 is 3 times more than the number of classical mp3. Let c represent the number of classical mp3. Write an expression of the number of rocks mp3s
Let the rock mp3 on Eric's computer be x.
Given the classical mp3 on Eric's computer be c.
Given the number of rocks, mp3 is 3 times more than the number of classical mp3.
[tex]\begin{gathered} x=3c+c \\ x=4c \end{gathered}[/tex]Twice u is 3 less than 5 times u. What is the value of u?
Given data:
The expression for the twice u is 3 less than 5 times u is,
2u=5u-3
3=3u
u=1
Thus, the value of u is 1.
Which of the following functions shows the quadratic parent function,F(x) = x?, horizontally stretched?
The parent function is,
[tex]F(x)=x^2[/tex]The graph is stretched horizontally when x is replaced by kx where k is less than 1.
Thus, option (B) is the correct solution as x is replaced by x/2 in the F(x) to get G(x).
The red curve represents F(x) and the blue one represents G(x).
58.165 to the 1st significant figure
Answer:
60
Step-by-step explanation:
The first significant figure is 5. Since the second number is 8 (greater than or equal to 5), the 5 rounds up to a 6. Thus the number becomes 60.
if the age of a tree was predicted to be 800 years old using the regression equation y equals 4.39 x - 6.77 what is the diameter have to be ? this is my 5th time asking a Tudor it does not seem like no one knows how to answer this question
We can use the equation:
[tex]age=\text{circumference}+\text{growth rate}[/tex]Age is given as 800
Circumference is 2*pi*r
Growth rate is the rate of change of growth of the tree. We can find this by looking at the linear equation.
The equation is:
y = 4.39x - 6.77
Matching with y = mx + b, we can say:
m = 4.39 [m is the rate of change. So, this is the growth rate]
Now, we substitute into equation to solve for r:
[tex]\begin{gathered} 800=2\pi r+4.39 \\ 800-4.39=2\pi r \\ 795.61=2\pi r \\ r=\frac{795.61}{2\pi} \\ r=1249.74 \end{gathered}[/tex]Diameter is double this radius. So,
Diameter = 1249.74 * 2 = 2499.48
Diameter = 2499.48
z=9x^2-y find the value of z when x=3 and y=9
Answer:
it's 72
Step-by-step explanation:
z = 9х^2 - у , when x = 3, y = 9, we'll get
z = 9* 3^2 - 9.
9 * 3^2 - 9 = 9*9-9 = 81 - 9 = 72
So, z = 72
The degree of x^2 + x - 4 is 3 true or false?
Given
[tex]x^2+x-4[/tex]The degree of a polynomial is the greatest exponent of x. In this case, the greatest exponent of x is 2.
Answer: false
Your neighborhood movie theater has a 25-foot-high screen located 8 feetabove your eye level. If you sit too close to the screen, your viewing angle is toosmall, resulting in a distorted picture. By contrast if you sit too far back, theimage is quite small, diminishing the movie's visual impact. If you sit & feet backfrom the screen, your viewing angle is given by0 = tan-1 33-tan-11) Choose a value for ærepresenting how far back you want to sit in feet and usethe formula above to calculate the viewing angle 8 for that distance. Make sureyour calculator is in radian mode.2) Go to Movie Theater Mewing Angle and compare your choice of distance tothe optimal choice of distance. How close or far are you to the optimal(maximum) viewing angle?3) What is your viewing angle in degrees? (convert your angle to the nearesttenth)
1. We are given that the angle is determined by the formula
[tex]\theta=tan^{\text{ - 1}}(\frac{33}{x})-tan^{\text{ -1 }}(\frac{8}{x})[/tex]lets say we want to sit at x = 25 feet. So if we replace x with 25 and we plug it in our equation, using a calculator in radians we get
[tex]\theta=tan^{\text{ -1}}(\frac{33}{25})-tan^{\text{ -1}}(\frac{8}{25})\text{ = }0.61276\text{ radians}[/tex]3. To transform one angle that is in radians, to degrees, we must mutiply by 180° and divide by pi radians. So, in our case we get
[tex]\theta\text{ = 0. 61276}\cdot\frac{180}{\pi}\text{ = }35.1086\text{ degrees}[/tex]Answer the following.(a) Find an angle between 0° and 360° that is coterminal with 1260°(b) Find an angle between 0 and 2pi that is coterminal with-23pi/12Give exact values for your answers.
Answer:
[tex]\begin{gathered} a)\text{ 180 deg} \\ b)\text{ }\frac{\pi}{12} \end{gathered}[/tex]Explanation:
a) Here, we want to find an angle between 0 and 360 degrees that is coterminal with 1260
To find angles coterminal with an angle, what we have to do is to subtract multiples of 360 degrees from it
Now, let us find the number of times we can have 360 in 1260
By division, we have it that 1260/360 = 3.5
Now, to find the coterminal angle within the range, we have it that:
[tex]1260-3(360)\text{ = 1260-1080 = 180}[/tex]The coterminal angle within the given range is 180 degrees
b) Mathematically, we know that the term "pi" represents 180 degrees
Thus 2 pi is same as 2 * 180 = degrees
For ease of convenience, let us have the angle given in degrees
We have this as:
[tex]\frac{23\times180}{12}\text{ = -345 }[/tex]Now, let us proceed
What we have to do is to add this to 360 degrees so we can get the positive coterminal in degrees
We have this as -345 + 360 = 15
Lastly, we represent this in radians as follows:
[tex]\frac{\pi}{12}[/tex]
Mark simplified the equation 36 – 7x = -7(x -7(x - 5) to36 – 7x = -7x + 35. This means that the equation has:A. only 1 solutionB. no solutionsC. infinitely many solutions
We are to simplify the given equation to determine if it has 1 solution, no solution or infinitely many solutions.
So,
If 36 - 7x = -7(x - 5) to 36 - 7x = -7x + 35.
Let's work on the second equation.
36 - 7x = -7x + 35
First let's collect like terms.
36 - 35 = -7x + 7x
From what we can see the equation, -7x + 7x will cancel out.
Therefore, there are no values of x that makes the equation true.
So, there is No Solution.
The correct option is B, which is No Solution.
Find anequation for the vertical line through the point (-5, -3).
A line is vertical, then all points lie on it have the same x-coordinates
If line L is a vertical line and passes through the point (a, b), then its equation is
[tex]x=a[/tex]Since the given line is a vertical line and passes through the point (-5, -3)
That means a = -5
Then its equation is
[tex]x=-5[/tex]1. An aero plane flies due north from a town T on the equator at a speed of 950 km/h for 4 hours to another town X. It then flies eastwards to town Y on a longitude 65°E. If the longitude of T is 15°E. a. Represent this information on a diagram b. Calculate the: (i) Latitude of X, correct to nearest degree (ii) Distance between X and Y, correct to four significant figures 22 [Take = and radius of the earth = 6400 km] 7