Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test.




How long did Jordan spend studying for each test?



134 hours



35 hour



15 hour



123 hours

The true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.

To find the true solution(s) to the equation, we need to solve for x and check if the obtained solutions satisfy the original equation. The extraneous solution(s), if any, will be the solutions that do not satisfy the original equation.

To solve the equation, we can start by isolating one of the square root terms. Rearranging the equation, we have:

[tex]\sqrt{x + 5} = 3 + \sqrt{x}[/tex].

The equation can be evaluated as:

[tex]\sqrt{x + 5} - \sqrt{x} &= 3 \\(\sqrt{x + 5})^2 &= (3 + \sqrt{x})^2 \\x + 5 &= 9 + 6\sqrt{x} + x \\6\sqrt{x} &= -4 \\\sqrt{x} &= \frac{-2}{3} \\x &= \frac{4}{9}\end{align*}[/tex]

Therefore, the true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.

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The complete question:

Solve the following equation and identify the true solution(s) as well as the extraneous solution(s):

[tex]\sqrt{x + 5} - \sqrt{x} = 3[/tex].

The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is: x * (1 - 1/8).

An expression in mathematics is a combination of numbers, variables, and operations that represent a value or set of values.

The expression calculates the reduction of x by 1/8 of x by subtracting 1/8 of x from x, which is x * 1/8. By subtracting this from x, the expression calculates x reduced by 1/8 of x. The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is:

x * (1 - 1/8).

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Answer: no, not a function

Step-by-step explanation: 0 is in the input twice, and if it were a function, it would only be there once. every input can only have one output

The solution to the inequality is (b) x > -2

From the question, we have the following parameters that can be used in our computation:

4.5x + 6 > -3

Collect the like terms

So, we have the following representation

4.5x > - 3 - 6

Evaluate the like terms

This gives

4.5x > -9

Divide both sides by 4.5

x > -2

Hence, the solution is (b) x > -2

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In ΔRST, the measure of angle R is  73.1°

Let us assume that r represents the opposite side of ∠R, and 't' represents the opposite side of ∠T

i.e., r = side ST and t = side RS

We know that the law of sine for triangle states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

i.e., for triangle ABC,

[tex]\frac{sin~A}{a} =\frac{sin~B}{b} =\frac{sin~C}{c}[/tex]

Using sine law for ΔRST,

[tex]\frac{sin~R}{r} = \frac{sin~S}{s} =\frac{sin~T}{t}[/tex]

Consider equation,

[tex]\frac{sin~R}{r} =\frac{sin~T}{t} \\\\\frac{sin~R}{79} = \frac{sin~(58)}{70}[/tex]

79 × 0.8481 = sin(R) × 70

sin(R) = 66.99 / 70

sin(R) = 0.9571

∠R = arcsin(0.9571)

∠R = 73.1°

Thus, measure of angle R = 73.1°

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The person who is correct is Matty: (12x 0.75) + (2x 1.2 =11.4  (second option)

The total pound of cheese is the total amount of of cheese used for cheeseburgers and the total amount of cheese wasted.

Total pounds of cheese = total pounds used for cheeseburgers + total cheese wasted

= (pounds of cheese needed for one cheeseburger x number of cheeseburger) + (number of waiters x pounds of cheese dropped)

= (12 x 3/4) + (1.2 x 2)

= 9 + 2.4

= 11.4 pounds

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1. The function for this problem is given as follows: f(x) = x - 3.

2. The numeric value of the function at x = 2 is of f(2) = -1.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define the function in this problem as follows:

f(x) = x - 3.

The numeric value at x = 2 is found replacing the lone instance of 2 by 2, hence:

f(2) = 2 - 3

f(2) = -1.

We attribute the function in this problem as f(x) = x - 3.

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the value of x, y, and z are 2√14, √74, and √252.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, the right triangle that has two other right triangles inside it:

From the Pythagorean theorem:

Hyppotaneus ² = height ² + base²

from the Bigger triangle:

H = 14 + 4 = 18

b = y

h  = x

Thus,

y² + z² = 18*18

y² + z² = 324.....(1)

from the triangle with a height of 14,

z² = x² + 14²

z² = x² +  196....(2)

From the triangle with the base of 4:

y² = x² +  16...(3)

For equations 2 and 3 substitute the value in equation 1

2x² + 212 = 324

2x² = 112

x² = 56; x = 2√14

Thus,

y² = 56 +16

y² = 74; y = √74

z² = 56 + 196

z² = 252; z = √252

Therefore, the value of x, y, and z are 2√14, √74, and √252.

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So, the height of the tower is approximately 363.6 feet.

You can use trigonometry to solve this problem.

If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.

We can use the tangent function to relate the angle of elevation to the height and distance.

tan(67) = h/d

We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.

h = d * tan(67)

h = 200 * tan(67)

The height of the tower is approximately 363.6 feet.

Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.

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Answer: The answer is 5 units

Step-by-step explanation:

If you plot it on a graph and what not it comes out to 5 units, going diagonally.

In a city, the distance between the library and the post office is three units. This may be calculated by counting the gaps between the two points on the grid illustrated above. The Library is in position 1 and the Post Office is in position 4, therefore the distance between them is three units.

The amount of space between two locations is defined as distance. It is commonly measured in meters, kilometers, miles, or feet. Distance is used to compute the length of a journey, the time required to go a specific distance, and the speed of an item moving a specific distance. It may also be used to determine the dimensions of an item. In trigonometry, distance is also used to measure angles, such as the angle between two points on a circle. Distance may be present in practically every facet of our daily lives, from city distances to item sizes. Distance is an important term to grasp in both physics and mathematics.

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For the quadratic equation -2x²+12x-13, the range is option D: All real numbers less than or equal to 5.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The values for x and h(x) are given in the table.

Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.

The range of h, h(x), in the table given are all real numbers.

The quadratic equation from the points in the table can be deduced as -2x²+12x-13.

The maximum of the graph is at (3,5).

For a parabola ax²+bx+c with Vertex (xv,yv) -

If a<0, then the range is f(x) ≤ yv.

If a>0, then the range is f(x) ≥ yv.

Since, a = -2, then f(x)≤ 5.

Therefore, the range values of h is f(x)≤ 5.

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Answer:

1. a > 6

2. a = 6

3. 0 < a < 6

4. a is divisible by 6

Answer:
1. a>6 the answer could be, 7, 8, 9, 10 and it keeps going on.
2. the answer is 6

3. a<6 the answer is anything below 6 so 5, 4, 3, 2, 1, and more.

4. anything that is a multiple of 6 is true. like 6, 12, 18, 24, 30, 36, and it keeps going.

The radius of the circle is approximately =71.96 units

Circles can be defined by their radii and all points on the circumference of a circle are equidistant from the center. Circles are widely used in mathematics, science and engineering for various applications, including modeling and solving problems in geometry.

The formula for the circumference of a circle is 2 * pi * r, where r is the radius.

Given the circumference, we can solve for the radius:

452.16 = 2 * pi * r

r = 452.16 / (2 * pi)

The radius of the circle is approximately 71.96 units.

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The number of customers are not exactly same in two cases.

In mathematics →

Given is the -

Number of customers this month -

{x} = 250 - {12% of 250}

{x} = 250 - {12/100 x 250}

{x} = 250 - 12 x 2.5

{x} = 250 - 30

{x} = 220

Number of customers last month -

250 = {x} + {12% of x}

250 = {x} + (12/100){x}

250 = {x} (1 + 3/25)

250 = {x} (28/25)

{x} = (250 x 25/28)

{x} = 223 {approx.}

Therefore, the number of customers are not exactly same in two cases.

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Answer:110

Step-by-step explanation: Add 7 shingles every row you go up.

Row 1=75

2=82

3=89

4=96

5=103

6=110

Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

According to 43% of eighth graders, they spend more than an hour a day on social media.

A ratio stated as a fraction of 100 is what is meant by the term %. Students were asked in a poll if they thought they spent more or less time per day on social media.more less , 7th 12 14 , 8th 20 ,26 . The number of students who responded "more" must be divided by the total number of 8th graders polled in order to arrive at the %, which must then be multiplied by 100.

This percentage is the proportion of 8th graders who believe they spend more than an hour each day on social media.Twenty of the forty-six students (20+26) responded "more," or roughly 43.48 percent. As a result, 43% of eighth graders claim to spend more than an hour every day on social media.

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1. In parallelogram ABCD, the sum of ∠a and ∠b is 180 degree. So the option d "a° + b° = 180°" is correct.

2. In rectangle FGHK, FC = CH = 8. 5 cm, then the area of rectangle FGHK is 120 square cm. So the option b is correct.

3. The length of GK is 17 cm because the length of all diagonal is same in rectangle. So the option d is correct.

4. In parallelogram EFGH, the sum of ∠e and ∠f is 180 degree. So the option d "a° + b° = 180°" is correct.

1. In parallelogram ABCD, ∠a and ∠b are adjacent to each other.

So, AB║DC.

Then we get ∠a and ∠b as subsequent interior angles, both of which need to be added.

So the sum of ∠a and ∠b is 180 degree.

a° + b° = 180°

2. In rectangle FGHK, FC = CH = 8. 5 cm.

From the diagram, FG = 8 cm

FH = FC + CH

FH = 8.5 + 8.5

FH = 17 cm

Using Pythagorean Theorem to find the value of GH.

FH^2 = FG^2 + GH^2

(17)^2 = (8)^2 + GH^2

289 = 64 + GH^2

Subtract 64 on both side, we get

GH^2 = 225

Taking square root on both side, we get

GH = 15 cm

The area of rectangle = FG × GH

The area of rectangle = 8 × 15

The area of rectangle = 120 square cm

3.  In rectangle FGHK, FC = CH = 8. 5 cm.

So FH = FC + CH

FH = 8.5 + 8.5

FH = 17 cm

As, a rectangle is split into two congruent right triangles by a diagonal. The length of the rectangle's diagonals are all the same.

So GK = FH = 17 cm

4. In parallelogram EFGH, ∠e and ∠f are adjacent to each other.

So, EF║HG.

Then we get ∠e and ∠f as subsequent interior angles, both of which need to be added.

So the sum of ∠e and ∠f is 180 degree.

e° + f° = 180°

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Answer:

10 times larger.

The 3 in 903.7 is in the ones place, and the 3 in 4.31 is in the tenths place, which is to the left of the decimal one time.

If you were to move the 3 in 4.31 to the right of the decimal like where the 3 is in 903.7, then you would be increasing the 3s value by 10.

Step-by-step explanation:

Hope it helps! =D

Answer:

  $340

Step-by-step explanation:

You want to know the original price of a desk priced such that $272 is 80% of its original price.

We can write the relation as an equation. If p represents the original price, then we have ...

  $272 = 80% × p

  p = $272/0.80 = $340 . . . . . . . divide by the coefficient of p

The original price is $340.

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The answer to the inequality system is y > 2 – x, y < -1

Step 1: Formulate each inequality as y = x + b.

(1) x + y > 2

(2) 2x – y > 1

(3) y > 2 - x Each side of the equation had x subtracted (1)

-y > 1 - 2x 2x were taken out of either side of 2.

(4) y < 2x – 1 -1 multiplied each side, then the inequality was turned around.

Graphing the functions as equalities in step two

(5) y = 2 – x

(6) y = 2x - 1

The borders of the inequalities will be formed by the lines. On one side of a line, the condition will be true, but not on the other (see the diagram below).

Step 3: Highlight the graphs' areas where the inequalities exist.

The graph of y > 2 - x is shown by the red line.

Shade the area above the line because y exceeds a value on the high side of the line (red).

The graph of y = 2x - 1 is shown by the blue line.

Shade the area below the line because y is less than a value on the line's low side (blue).

Any location where the colored regions overlap constitutes the solution set for both inequality problems (purple).

4. Check the outcome.

Input a point in the shaded region, such as (2, 2), and confirm that each inequality is true.

(1) x + y > 2 (2) 2x – y >1

2 + 2 > 2 2(2) – 2 > 1

4 > 2 4 – 2 > 1

2 > 1

It verifies.

The answer to the inequality system is

y > 2 – x, y < -1.

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Correct option is A, (1,2) is the correct option for the given system of equations.

Equations occurring simultaneously, system of equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system).

For a system to have a single solution, the number of equations must equal the number of unknowns.

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

A system of equations is a collection of equations with one or more variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.

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Answer:

Step-by-step explanation:

To find the slope of the tarp, we can use the concept of rise over run, which is the ratio of the vertical change (the rise) to the horizontal change (the run). In this case, the rise is the distance from the corner of the tarp to the top of the pole, and the run is the distance from the corner of the tarp to the bottom of the pole.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle formed by the corner of the tarp, the bottom of the pole and the top of the pole.

The length of the hypotenuse is the distance from the corner of the tarp to the top of the pole and the length of the adjacent side is the distance from the corner of the tarp to the bottom of the pole.

We know that:

adjacent side = 10 ft

Hypotenuse = h

Applying the Pythagorean theorem:

h^2 = 10^2 + 6^2

h = √(10^2 + 6^2)

h = √(100 + 36) = √136 = 11.66 ft

Now we can calculate the slope:

slope = rise/run = (h-10) / 6

slope = (11.66-10) / 6 = 1.66/6 = 0.277

So the slope of the tarp from the corner to the top of the pole is 0.277 or approximately 0.28.

7. To show that VRHK is a square, one can observe that the opposite sides of the quadrilateral, VR and HK, are equal in length and the two adjacent sides, RH and VK, are also equal in length.

8. For VRHK to be a square, z must equal √2, so that VC = 6√2 and

VR = 12.

9. The length of RK is 12√2

10. The length of VK is 12√2

Solution:

8. We can solve this problem by using the Pythagorean Theorem. We know that the sides of a square are equal, so we can set up an equation using the theorem. VC = 6z, VR = 12, and we want the hypotenuse, VRHK, to be a square. VH² = VR² + RH² = 12√2.

VC = 6z = VH/2 = 12√2/2 = 6√2

6z = 6√2

z = √2

9. The length of RK' =  s√2 =12√2

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The room with the given dimensions has a volume of 316, 516, 800 cm^3.

The volume of a room is a measure of the amount of space inside it, and it is calculated by multiplying the length, width, and height of the room.

In this case, the room has dimensions of 9.15 meters by 9.4 meters by 3.68 meters.

To find the volume of the room in cm^3, we first need to convert the dimensions of the room from meters to centimeters.

1 meter is equal to 100 centimeters, so

9.15 meters is equivalent to 915 centimeters,

9.4 meters is equivalent to 940 centimeters,

and 3.68 meters is equivalent to 368 centimeters.

Once we have the dimensions in centimeters, we can calculate the volume by multiplying the length, width, and height:

915 cm x 940 cm x 368 cm = 316, 516, 800 cm^3.

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Yes, it is worth the extra drive to going the far store for buying the chicken. The difference between the both store worth is about $1.24.

We have to buy some chicken for dinner tonight. We found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than our usual neighborhood store, which sells it for $3.19 a pound.

$3.09 ×3 = $19.14 (far store)

$3.19 × 3 = $20.34 (near store)

For the neighbourhood store :

Distance = 2.3 mile

Multiply by 2 because we not only have to drive there, but also back home for the round trip: so, total distance = 2.3 miles × 2 = 4.6 miles

As car average is 19 miles per gallon

= 4.6 mile/ 19 miles per gallon

= 0.24 gallon < 13 gallons

Now, costs to travel to each store from the gas used. Cost of gas is $3.62/gallon,

total cost = 0.2421 gallons×$3.62 /gallons = $0.88

Similarly for far store : distance from home to store = 8.7 miles but take double of it we get, 8.7 miles × 2 = 17.4 miles

As car average is 19 miles per gallon

= 17.4 miles /19 miles per gallons

= 0.915 gallons < 13 gallons

The cost of gas for the respective trip = 0.915 gallons × $3.62 /gallons = $3.32

Now, let's add the gas and chicken costs together to get total worth

$19.14 + $3.32 = $22.46 to the far store

$20.34+ $0.88 = $21.22 to the near store

Hence, the worth in travelling far store is greater than neighbourhoid store.

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Complete question:

You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.19 a pound. Is it worth the extra drive? First, determine what information you need to answer this question, then click here to display that info (along with other info).

How much chicken will you be buying? 3 pounds

How far apart are the two stores? My neighborhood store is 2.3 miles away, and takes about 8 minutes. The store across town is 8.7 miles away, and takes about 25 minutes.

How kind of mileage does your car get? It averages about 19 miles per gallon in the city.

How many gallons does your car hold? About 13 gallons

How much is gas? About $3.62/gallon right now.

Yes, it is worth the extra drive to the far store to get the chicken. The value of the two stores varied by around $1.24.

To make chicken for dinner tonight, we must purchase some. We discovered an advertisement indicating that the supermarket across town is selling it for $3.09 per pound, which is less expensive than our typical neighborhood grocery, which charges $3.19 per pound.

Compare the prices of chicken: We would pay for the 3 pounds of chicken that we require.

$3.09 ×3 = $19.14 (far store)

$3.19 × 3 = $20.34 (near store)

Let's look at the expense of driving in our car:

For the local retailer: = 2.3 miles away

Because we need to travel both ways, we must double the distance by two, making the total distance 2.3 miles x 2 = 4.6 miles.

Since the average automobile gets 19 mpg

19 miles per gallon/4.6 miles = 13 gallons x 0.24 gallons

Now, add the cost of gas used to drive to each store. Gas costs $3.62 per gallon.

Total cost = 0.2421 gallons at a cost of $0.88 per gallon.

The same goes for a far store:

the distance from home to the store is 8.7 miles, but if we double that by two, we get 17.4 miles.

Since the average automobile gets 19 mpg = 17.4 miles per gallon /19 miles per mile

13 gallons equals 0.915 gallons.

The gas price for the relevant journey is 0.915 gallons times $3.62 a gallon, or $3.32.

To determine the overall cost,

let's now combine the costs of the chicken and petrol.

$22.46 to the far store from $19.14 plus $3.32

$20.34 plus $0.88 equals $21.22 for the nearby retailer.

Therefore, a far store is more valuable than a nearby store. The difference is $1.24

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The m∠EXD and m∠AXE are the supplementary angles.

The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°. The value of x in the figure is 113°

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

01)

Two angles will be linear pairs if their sum is 180°.

If the first angle is 62° then the second will be 180° - 62° = 118°

Hence "The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°".

02)

The angle x is in the same line with supplementary angle 67° so

x = 180 - 67 = 113°.

Hence "The value of x in the figure is 113°".

03)

In the figure, AXD is a straight line, therefore,

m∠EXD +  m∠AXE  = 180°

Since the sum of two angles is 180° then they are called supplementary angles.

Hence "The m∠EXD and m∠AXE are the supplementary angles".

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Blood types A and AB are receivers from someone with type A blood donors.

What is blood type?

There are four major blood groups determined by the presence or absence of two antigens, A and B, on the surface of red blood cells. In addition to the A and B antigens, there is a protein called the Rh factor, which can be either present (+) or absent (–), creating the 8 most common blood types (A+, A-,  B+, B-,  O+, O-,  AB+, AB-).

Someone with blood type A can donate blood to individuals with blood types A and AB.

This is because type A blood has the A antigen on the red blood cells and type AB has both A and B antigens.

While type A blood doesn't have the B antigen which is present in type B and AB blood, so it cannot be donated to those with type B or type B.

It's important to note that there are also positive and negative blood types, which are determined by the presence or absence of the Rh (Rhesus) antigen on the red blood cells.

So, someone with type A negative blood can only donate to individuals with type A negative or type AB negative blood.

Therefore, for A type blood donors can donate to A and AB blood type.

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The rectangular solid with the maximum volume would be a cube.

The surface area of a cube = 6A,

where A = the area of any one side

hence, the area of one side = 150/6 = 25 sq in.

The length of one face,

L = 25^0.5 = 5 in.

The volume, V of a cube = L^3.

Surface area

Surface area is the amount of space covering the outside of a three-dimensional shape.

volume

Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.

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Answer 0.000032 km

Step-by-step explanation: divide