All categories

3 years ago

please help im having such a hard time :( does this equation have no solution one solution or infinite solutions

Mathematics

2 answers:

WINSTONCH [101]3 years ago

8 0

One solution!

Step-by-step explanation:

If we make a graph of the given equations, the lines will intersect at a point. We know that whenever lines intersect, it means the equations have one solution or a unique solution.

VladimirAG [237]3 years ago

6 0

Answer:

One solution

Step-by-step explanation:

They don't end up on the same line to be infinite, therefore, it only has one solution

You might be interested in

At Friday's football game, 1,294 tickets were sold for a total amount of $8,816.00. If each student ticket costs $5.00, and each

NeTakaya

Answer:

512 student tickets.

Step-by-step explanation:

Let x be number of student tickets and y be number of adult tickets.

We have been given that at Friday's football game 1,294 tickets were sold. We can represent this information as:

$x+y=1294...(1)$

We are also told that each student ticket costs $5.00, and each adult ticket costs $8.00 and 1,294 tickets were sold for a total amount of $8,816. We can represent this information as:

$5x+8y=8,816...(2)$

From equation (1) we will get,

$y=1294-x$

Substituting this value in equation (2) we will get,

$5x+8(1294-x)=8,816$

$5x+10352-8x=8,816$

$-3x+10352=8,816$

$-3x=8,816-10352$

$-3x=-1536$

$x=\frac{-1536}{-3}$

$x=512$

Therefore, 512 student tickets were purchased at Fridays football game.

6 0

3 years ago

An expression is given (3^2)^3•3^6/3^4

Tomtit [17]

Hopes this if it doesn’t I any so sorry if I got it wrong:

Answer: 6561

7 0

3 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

3 years ago

The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical

True [87]

Answer: is it on chart? if count rise over run

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Some of Mrs. Turay’s eighth graders took the PSAT test. Score totals of ten of her students are below. Calculate the mean and th

den301095 [7]

Answer:

(a) Mean=74

(b) Median=70

Step-by-step explanation:

We have been given a data set of PSAT scores of Mrs. Turay's eight graders. We are asked to find mean and median of the given data set.

(a) Let us find mean of data set by dividing the sum of given scores by the number of students.

$\text{Mean}=\frac{60+62+67+69+70+70+71+75+76+120}{10}$

$\text{Mean}=\frac{740}{10}=74$

Therefore, the mean test score will be 74.

(b) Now let us find median of our given data set. We have been given that number of students is 10, therefore, our median will be the average of 5th and 6th term.

60, 62, 67, 69, 70, 70, 71, 75, 76, 120.

We can see that 5th term is 70 and 6th term is 70 as well.

$\text{Median}=\frac{70+70}{2}$

$\text{Median}=\frac{140}{2}$

$\text{Median}=70$

Therefore, the median test scores will be 70.

(c) We can see that our data set has an outlier score as 120, which has increased the mean. Mean score is greater than median score. Since median is not affected by extreme value outliers, therefore, median will be the best measure of center for given test scores.

3 0

3 years ago

Read 2 more answers