Answers
Answer:
x = 5
Step-by-step explanation:
The line segment divides the sides in proportion, that is
[tex]\frac{14}{10}[/tex] = [tex]\frac{2x-3}{x}[/tex] ( cross- multiply )
10(2x - 3) = 14x ← distribute left side
20x - 30 = 14x ( subtract 14x from both sides )
6x - 30 = 0 ( add 30 to both sides )
6x = 30 ( divide both sides by 6 )
x = 5
Related Questions
Victoria has a health care plan with a prescription benefit that offers four different options.
Option A: $55 monthly premium and $20 co-pay per prescription
Option B: $60 monthly premium and $15 co-pay per prescription
Option C: $65 monthly premium and $25 co-pay per prescription
Option D: $50 monthly premium and $30 co-pay per prescription
If Victoria fills an average of five prescriptions each month, which option is the least expensive? (4 points)
Option A
Option B
Option C
Option D
Answers
Answer:
OPTION B
Step-by-step explanation:
To solve, create a formula.
y= 5(copay)+premium
Using this you get:
Option A: 5(20)+55= $155
Option B: 5(15)+60= $135
Option C: 5(25)+65= $190
Option D: 5(30)+50= $200
Answer:
Option B
Step-by-step explanation:
Option A : 55 + 20(5) = 155
Option B : 60 + 15(5) = 135
Option C : 65 + 25(5) = 190
Option D : 50 + 30(5) = 200
A fruit stand has to decide what to charge for their produce. They need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 oranges. We put this information into a system of linear equations.
Answers
Answer:
3.30 for apple and 2.00 for an orange
Step-by-step explanation:
To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. We can then solve this system using the elimination method to find the cost of an apple and an orange.
Explanation:To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. Let's use x to represent the cost of an apple and y to represent the cost of an orange.
From the given information, we can set up the following equations:
111x + 111y = 5.30
111x + 222y = 7.30
Next, we can solve this system of equations by using substitution or elimination. Let's use the elimination method:
Multiply the first equation by 2, and multiply the second equation by 1:
222x + 222y = 10.60
111x + 222y = 7.30
Subtract the second equation from the first:
111x = 3.30
Divide both sides by 111:
x = 0.03
Substitute this value back into either equation to solve for y:
111(0.03) + 222y = 7.30
3.33 + 222y = 7.30
222y = 3.97
y = 0.01
Therefore, the cost of an apple is $0.03 and the cost of an orange is $0.01 at the fruit stand.
When completely factored, 3x2−48 equals -
Answers
Final answer:
The quadratic expression 3x^2-48 can be completely factored as 3(x-4)(x+4) by first factoring out the common factor and then utilizing the difference of squares.
Explanation:
To factor this expression completely, we first need to look for common factors and any patterns that might help simplify the expression. Both terms in the expression 3x2−48 have a common factor of 3. Factoring out this common factor gives us:
3(x2 − 16)Notice that the expression inside the parenthesis, x2 − 16, is a difference of squares, which can be factored further into (x − 4)(x + 4). Therefore, the fully factored form of the original expression is:
3(x − 4)(x + 4)This shows how identifying common factors and utilizing the difference of squares helps in completely factoring the given expression.
Determine the equation of the graph.
Answers
Answer: C
y=-5cos(x) is the graphed equation. Cos(x) starts at (0,0) and one period is 2pi or 6.28 and by cos(x) multiplied by -5 starts the cosine wave at (0,-5) and thus corresponds to the graphed equation shown.
Any questions please feel free to ask. Thanks
The radius of Earth is about 3960 miles. The radius of the moon is about 1080 miles. a. Find the surface area of Earth and the moon. Round your answer to the nearest tenth of a million. The surface area of the Earth is about million square miles and the surface area of the Moon is about million square miles. b. Compare the surface areas of Earth and the moon. Round your answer to the nearest tenth. The surface area of the Earth is about times greater than the surface area of the moon. c. About 70% of the surface of Earth is water. How many square miles of water are on Earth’s surface? Round your answer to the nearest tenth of a million. There are about million square miles of water on the Earth's surface.
Answers
A) The formula for surface area of a sphere is A = 4*PI*r^2
using 3.14 for PI:
Surface area for Earth = 4 * 3.14 x 3960^2 = 196,960,896 miles^2
Surface area of the moon: 4 * 3.14 * 1080^2 = 14,649,984 miles^2
B)Divide the Surface of the Earth by the moon:
196,960,896 / 14,649,984 = 13.44
The Earths surface is 13.4 times larger than the moon.
C) Multiply the surface of the Earth by 70%:
196,960,896 * 0.70 = 137,872,627.2 million square miles of water.
Calculating surface areas of Earth and the moon, comparing them, and determining the amount of water on Earth's surface.
a. Find the surface area of Earth and the moon:
Surface area of Earth = 4 x π x (3960 miles)2 ≈ 196.9 million square milesSurface area of Moon = 4 x π x (1080 miles)2 ≈ 14.6 million square milesb. Compare the surface areas of Earth and the moon: Earth's surface area is approximately 13.5 times greater than the Moon's surface area.
c. About 70% of Earth's surface is water: There are approximately 137.9 million square miles of water on Earth's surface.
Please help me!!!!!!!!!!!
Answers
90 degrees
3 ( square root sign) 10
10√2
Then b = ------------ = 5√2
Answer:
5√2
Step-by-step explanation:
Notice that the sine function links side b, the hypotenuse (10) and the 45° angle:
1
sin 45° = ------ = b/10
√2
Then b = 10√2 / 2 = 5√2
Jeremy and Caitlin collect baseball cards. The ratio of Jeremy's cards to Caitlin's cards was 9 to 3. After Jeremy gave 12 cards to Caitlin, they had an equal number of cards. How many cards did Caitlin and Jeremy have at first? Explain.
Answers
Caitlin will have 18 and Jeremy will have 6 at first because then 18-6=12 which is how many cards Caitlin have to Jeremy
There are two numbers, one is 7 more than twice the other. The sum of the numbers is 43. Make the equation to find the smaller number. Find the two numbers. Answer: If the smaller number is x, the equation will be . The numbers in ascending order are and .
Answers
Answer:
the numbers are 12, 31
Step-by-step explanation:
Give an example of a ratio that is not a rate. Tell why it is not a rate.
Give an example of a ratio that is also a rate. Tell why it is a rate.
Answers
Answer:
Ratio is it rate. Can you do the rate of numbers.
For example, if we say: If the car was very high to acceleration at least, 1,000 km/h.
If Usain Bolt was won on the Olympics, he has 27 km/h.
Hmm, the ratio isn't rate at all. This method can do the non rate. For example, if we say: If the gas price at BP, there's $100 per year.
Step-by-step explanation:
With this method, you must solve the ratio isn't rate.
For there's the group, this was what do you say, it's GCF, or greatest common factor. With this GCF method, for example: if we say, the European Parliament, and the MPs, are divided by gender, if we divide by male and female. For more examples, see the answer at the above with the picture
With this method of the rate, there are no of speed, price, or something else.
There are some examples like the km/h, representing the Kilometers per hour.
Hopefully with this helpful example
Four loan balances are $6,500, $3,600, $5,400, and $7,500, respectively. The current interest rates for the loans are 7%, 5%, 6%, and 9%, respectively. If the four are to be consolidated into one loan, what is the WEIGHTED AVERAGE interest rate on that loan?
A) 6.75%
B) 7.01%
C) 7.04%
D) 7.10%
Answers
[(455 + 180 + 324 + 675)/(65 + 36 + 54 + 75)] = 7.10
Answer is D.
Answer:
7.10% is the answer.
Calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y 2 − 2zi through the surface s parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v 2 with 0 ≤ u, v ≤ 1, and oriented by φu × φv
Answers
I'm not sure what to make of the "h" and "i" in your question, so I'll just ignore them (and the 3). Looks like we have
[tex]\vec f(x,y,z)=(x+y,x-y,x^2+y^2-2z)[/tex]
and a surface parameterzied by
[tex]\varphi(u,v)=(u+2v,u-2v,u^2+2v^2)[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Then
[tex]\varphi_u\times\varphi_v=(4u+4v,4u-4v,-4)[/tex]
so that the flux is given by the integral
[tex]\displaystyle\iint_S\vec f\cdot\mathrm d\vec S=\int_0^1\int_0^1(2u,4v,4v^2)\cdot(4u+4v,4u-4v,-4)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle8\int_0^1\int_0^1(u^2+3uv-4v^2)\,\mathrm du\,\mathrm dv=\boxed{-2}[/tex]
To calculate the flux of the given vector field through the surface S, you need to calculate the partial derivatives of the parametrization, then find the cross product of these partial derivatives, and finally evaluate the double integral over the surface using the flux formula.
Explanation:To calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y2 − 2zi through the surface S parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v2 with 0 ≤ u, v ≤ 1 and oriented by φu × φv:
Calculate the partial derivatives of φ(u, v) with respect to u and v.Calculate the cross product φu × φv using the partial derivatives obtained in the previous step.Plug the vector field f(x, y, z), the parametrization φ(u, v), and the cross product φu × φv into the flux formula Φ = ∫∫S f • (φu × φv) dA.Evaluate the double integral over the surface S using the limits of integration 0 ≤ u, v ≤ 1.Factor the following equation to find its zeros.
y = x^2 - 15x +36
A| 12,3
B| Cannot be factored
C| 12, -3
D| -12, -3
Answers
Answer:
A| 12, 3
Step-by-step explanation:
The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...
y = (x -12)(x -3)
A quick check shows this product is ...
y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required
The factors are zero when x is either 12 or 3.
The zeros of the equation are 12 and 3.
____
Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).
Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.
The area of the circular base of a cylinder is 36π square units. The height of the cylinder is 2 units.
What is the lateral area of the cylinder? Express the answer in terms of π.
12π square units
24π square units
60π square units
72π square units
Answers
Answer: second option.
Step-by-step explanation:
The formula used for calculate the lateral area of a cylinder is this one:
[tex]LA=2\pi rh[/tex]
Where "r" is the radius and "h" is the height
The formula for calculate the area of a circle (which is the base of a cylinder) is:
[tex]A=\pi r^2[/tex]
Knowing the area of the base, you can solve for the radius:
[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]
Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:
[tex]LA=2\pi (6units)(2units)[/tex]
[tex]LA=24\pi\ units^2[/tex]
Answer:
24π square units (edge)
Step-by-step explanation:
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 121212 feet^3 3 start superscript, 3, end superscript of fluffy material. What is the length of the pillow?
Answers
Answer:
The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?
The length of the pillow is 4 feet
Step-by-step explanation:
The formula of the volume of the wedge is [tex]V=\frac{1}{2}bhl[/tex] , where
b is the base of ith is the height of itl is the length of it∵ The pillow in the shape of a wedge
∵ The pillow is filled with 12 ft³ of fluffy material
∴ The volume of the wedge = 12 ft³
∵ The base = 3 feet
∵ The height = 2 feet
- Use the formula of the volume above to find its length
∵ [tex]V=\frac{1}{2}(2)(3)l[/tex]
∴ V = 3 l
∵ V = 12 ft³
- Equate 3 l by 12
∴ 3 l = 12
- Divide both sides by 3
∴ l = 4 feet
∴ The length of the pillow is 4 feet
Jamal is x years old. His mother is 28 years older than Jamal. Jamal's uncle is two times older than Jamal's mother. Write and simplify an expression that represents Jamal's uncle age in years
Answers
Answer:
From the information, we know that Jamal's mother is 28 years older than Jamal, so his mothers age should be:
x + 28 (years)
Also, we know that his uncle's age is twice as much as Jamal's mother age, so we have the following expression:
(x + 28) · 2 = 2x + 56
*Hope this help you
Jamal's uncle's age can be expressed as 2(x + 28), which simplifies to 2x + 56 years.
Jamal is x years old, and his mother is 28 years older than him. Therefore, his mother's age can be represented by x + 28. Jamal's uncle is two times older than Jamal's mother, which means we need to multiply his mother's age by 2 to get the uncle's age. So, the expression for Jamal's uncle's age is 2(x + 28). Simplifying this expression, we get:
2(x + 28)
2x + 2(28)
2x + 56
Thus, Jamal's uncle's age is represented by the expression 2x + 56 years.
The beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit. What is the cost of the basic kit
Answers
Answer:
45
it is what it is
The cost of basic hokey kit is $45.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit.
Let the cost of the basic kit be x.
Now, 3x+15=150
3x=135
x=$45
Therefore, the cost of basic kit is $45.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ5
Identify 2 objects you could find in a grocery store that holds less than 100 millimeters.
Answers
Answer:
a food container and a bowl
A person purchased 5k + 2 items for a total cost of 35k 2 + 29k + 6. Find the average cost per item of this purchase.
Answers
Answer:
[tex]\boxed{7k + 3}[/tex]
Step-by-step explanation:
Average cost = total cost/number of items = (35k² + 29k + 6)/(5k + 2)
Perhaps the best way to solve this problem is to use long division.
7k + 3
5k + 2)35k² + 29k + 6
35k² + 14k
15k + 6
15k + 6
0
Thus,
[tex]\frac{35k^{2}+29k+ 6}{5k + 2} = 7k+3[/tex]
The average cost per item is [tex]\boxed{7k+3}[/tex].
Answer:7k+3
Step-by-step explanation:
Rewrite the equation in polar form.
Answers
Answer:
C) √5(cos(117°) +i·sin(117°))
Step-by-step explanation:
The rectangular number a+bi can be written in polar form as ...
√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))
Here, we have a=-1, b=2, so the magnitude is ...
√((-1)^2 +2^2) = √(1+4) = √5
and the angle is ...
arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle
Then you have ...
-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"
_____
Comment on the answer
The "polar form" is generally written as ...
(magnitude)·(cos(angle) +i·sin(angle))
You may also see it as ...
(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"
In my engineering courses, we often used the form ...
(magnitude) ∠ (angle)
The form used by my calculator is ...
(magnitude)·e^(i·angle) . . . . . where angle is usually in radians
A train travels 480 miles at a constant speed (x), in miles per hour. Write an equation that can be used to find the speed of the train, if the time to travel 480 miles is 6 hours. you do not need to solve the equation
Answers
Answer:
480 = x(6)
Step-by-step explanation:
Given in the question that,
distance travelled by the train = 480 miles
time taken by the train to travel 480 miles = 6 hours
Suppose speed of train = x miles/hour
Formula to use to drive the equation
distance = speed x time480 = x(6)
x = 480/6
x = 80 miles/hour
The ratio of students who walk home from school to the students who ride the bus home is 2 : 7. The number of bus riders is how many times the number of students who walk home?
Answers
Answer:
3.5
Step-by-step explanation:
7/2=3.5
Answer:
3.5
Step-by-step explanation:
Ratio of
those who walk : those who ride = 2 : 7
This means that for every 2 students who walk, there are 7 students who ride
Therefore, for every 1 student that walks, (hypothetically) there are 3.5 (7/2) students who ride
Then the number of bus riders is 3.5 times the number of students that walk.
How do you find the center and the radius for [tex]x^{2} +y^{2} =25[/tex]?
Answers
Answer:
The center is (0,0) and the radius is 5
Step-by-step explanation:
To find the center of a circle, you need to look at the equation
In this case this equation could be written as
[tex](x-0)^2+(y-0)^2=5^2[/tex]
The x value is x=0 for the center and the y values is y=0
The radius can be found by looking at the constant that is squared, so r=5
In the case of an equation like this
[tex](x-1)^2+(y+1)^2=3^2[/tex]
The center point would be (1,-1) and r=3
What is the value for this expression? 2e-5
A.
0.0134
B.
296.826
C.
1.6375
D.
0.0034
Answers
Answer:
A. 0.0134
Step-by-step explanation:
This is a question that must be answered using a table or calculator. (Tables are not in general use these days.) See below for a calculator's output.
___
The answer would be 0.0135 if it were properly rounded.
The graph of f (0) = -4 cos 0 is shown below. The range of this function is
-4 ≤ f (0) ≤ 0
-π ≤ f (0) ≤ 2π
0 ≤ f (0) ≤ 2π
-4 ≤ f (0) ≤ 4
Answers
Answer:
-4 ≤ f ([tex]\theta[/tex]) ≤ 4
Step-by-step explanation:
The range of a function is the allowed y-values of the function.
We can simply look at the periodic function below and see that the y-value ranges from a negative 4 to a positive 4. It oscillates betwen -4 and 4. That is the range.
We can say -4 ≤ f ([tex]\theta[/tex]) ≤ 4
Last answer choice is right.
*** NOTE: it is a type, not "0", rather "[tex]\theta[/tex]"
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Vanessa has two bags that contain slips of paper. One bag has 4 slips of paper that are numbered 2, 3, 4, and 5. The other bag has 4 slips of paper that are numbered 3, 4, 5, and 6.
Vanessa chooses one slip of paper from each bag without looking.
The random variable X is the product of the numbers on the slips of paper.
What is P(12 ≤ X ≤ 15)?
Enter your answer, in simplest fraction form, in the box.
Answers
Answer: 5/16
Step-by-step explanation:
First, let's calculate the total number of possible outcomes:
4 options in the first bag and 4 options in the second bag = 16
Here is the list:
23 24 25 26
33 34 35 36
43 44 45 46
53 54 55 56
Next, calculate the total number of outcomes which result in the product of 12, 13, 14, or 15.
Here are their products:
6 8 10 12
9 12 15 18
12 16 20 24
15 20 25 30
There are 5 outcomes that include a product of 12, 13, 14, & 15.
Probability is: (# of satisfactory outcomes)/(total outcomes) = 5/16
What does the number 160 represent in the rational function that models the situation?
a) distance, in miles, between the cities
b) amount of fuel, in gallons, used by the train
c) time, in minutes, needed to travel between the cities
Answers
Answer:
the answer is A.
Step-by-step explanation:
Answer:
A) distance, in miles, between the cities
Step-by-step explanation:
correct on edge
Megan has 25 phone numbers stored in her cell phone. Abby has some phone numbers stored in her cell phone. Together they have a total of 61 phone numbers stored. If n= the number of phone numbers Abby has stored in her cell phone, which mathematical sentence expresses the information above?
Answers
Answer:
61-25=n
Step-by-step explanation:
Please select the best answer from the choices provided
Answers
Answer:
[tex]x=\frac{5\pi}{4}[/tex]
Step-by-step explanation:
We want to solve;
[tex]\cscx=-\sqrt{2}[/tex] in the 3rd quadrant
Recall that;
[tex]\sin x=\frac{1}{\csc x}[/tex]
We use the reciprocal ratio to get;
[tex]\sin x=-\frac{\sqrt{2}}{2}[/tex]
In the third quadrant the solution is
[tex]x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )[/tex]
[tex]x=\pi+\frac{\pi}{4}[/tex]
[tex]x=\frac{5\pi}{4}[/tex]
SOMEONE PLEASE HELP!!! 45 POINTS!!
Inscribed angles homework sheet for geometry
Answers
Answer:
h
Step-by-step explanation:
1.)Find the volume of a cylinder that has a radius of 1/2 and a height of 1.
2.) What is the volume of a sphere with a diameter of 11ft? Round your answer to the nearest cubic foot.
2786 cubic feet
5572 cubic feet
8359 cubic feet
6193 cubic feet
3.) Find the volume of a cone that has a radius of 1/2 and a height of 1.
answer choices :
1/12pie
3/2pie
3/4pie
1/6pie
Answers
Answer:
a.V=1.57
b. 2786 cubic feet (696.9)
c. 1/12 pie
Step-by-step explanation:
a. I have that the volume of a cylinder can be expressed as [tex]V= \pi r^{2} h[/tex] what would be the base (the area of the circle) by the height, so [tex]V=\pi * (\frac{1}{2}) ^{2} *1 =\frac{\pi }{2} = 1.57[/tex]
b. The volume of a sphere is given by the formula [tex]V=\frac{4}{3} \pi r^{3}[/tex] as the diameter is twice the radius I have to
[tex]V= \frac{4}{3} \pi (\frac{d}{2} )^{3} =\frac{4}{3} \pi (5.5)^{3} = 696.9[/tex]cubic feet the nearest cubic foot be 2786 cubic feet
c. The volume of a cone is given by the formula [tex]V=\frac{1}{3} \pi r^{2} h[/tex] so [tex]V=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \pi (\frac{1}{2} )^{2} *1=\frac{1}{3}\pi \frac{1}{4}=\frac{1}{12}\pi[/tex]