I need some help with math

Answer:

30

Step-by-step explanation:

To find the area of a triangle you need to multiply base times height. Which in this case is 6 times 10 equals 60. Then you just need to simplify it and it equals 30.

There are a few ways to solve this, the simplest of which is probably factoring. Start by finding factors of C (10) that add up to be B (-2).

fac(10) { -10, 1 ; -5, 2 }

Well, there are no factors of 10 that can add to b - so we will use the quadratic formula.

(-b +- sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -2, c = 10

b^2 - 4ac = (-2)^2 - 4(1)(10) = 4 - 40 = -36

-b +- sqrt(-36) / 2a

(2 +- sqrt(-36)) / 2

sqrt(-36)

sqrt(-1 * 36)

sqrt(-1) * sqrt(36)

i * 6

6i

2 + 6i / 2 ; 1 + 3i

2 - 6i / 2 ; 1 - 3i

Solutions: 1 + 3i, 1 - 3i

Answer:

x = 1± 3i

Step-by-step explanation:

x^2-2x+10=0

We can complete the square to solve by subtracting 10 from each side

x^2-2x+10-10=-10

x^2 -2x = -10

We need to add (2/2) ^2  to each side or 1

x^2 -2x+1 = -10 +1

x^2 -2x+1 = -9

The left side factors into (x- (2/2) ) ^2

(x-1) ^2 = -9

Take the square root of each side

sqrt((x-1) ^2 =± sqrt(-9)

x-1 = ±sqrt(-1) sqrt(3)

Remember the sqrt(-1) = i

x-1 = ± 3i

Add 1 to each side

x-1+1 = 1± 3i

x = 1± 3i

Answer: 9 gallons

Step-by-step explanation:

Set up the proportion, then multiply to solve for the variable.

[tex]\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=\dfrac{x}{72\ \text{pints}}[/tex]

[tex](72\ \text{pints})\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=(72\ \text{pints)}\dfrac{x}{72\ \text{pints}}[/tex]

[tex]\dfrac{36\ \text{gallons}}{4}=x}[/tex]

9 gallons = x

To convert pints to gallons, divide the number of pints (72) by the number of pints in a gallon (8), resulting in 9 gallons.

To determine how many gallons are the equivalent of 72 pints, we use the conversion factor that 1 gallon is equivalent to 8 pints.

First, we divide the given number of pints by the number of pints in a gallon:

Therefore, 72 pints is equivalent to 9 gallons.

Find the volume of the bath tub by multiplying all the dimensions together:

18 inches = 1.5 feet:

5 ft x 3 feet x 1.5 feet = 22.5 cubic feet.

The tub is 3/4 full so multiply the volume by 3/4 to find the amount of water in the tub:

22.5 x 3/4 = 16.875 cubic feet of water.

The tub drains at 1 cubic foot per minute, so it would take about 17 minutes to drain.    (16.875 rounded to the nearest whole minute).

Answer:

1915/22

Step-by-step explanation:

5745 / 66

Factor the numbers:

5745 = 3 * 1915

66 = 3 * 22

(3 * 1915) / (3 * 22)

Cancel the common factor:

1915/22

To divide 5,745 by 66, first determine how many times 66 fits into 574, then bring down the next digit and repeat. The result is 87 with a remainder of 3 or 87.068 as a decimal. The answer to 5,745 ÷ 66 is 87.068.

To find the result of 5,745 ÷ 66, follow these steps:

The answer to 5,745 ÷ 66 is 87.068.

Answer:

Cameron will make 15 baskets out of 50 tries.

Step-by-step explanation:

Since Annie can take out 18 baskets out of 30 and her brother can take out half as much, then we know that 18:2 is 9, so we know that Cameron can take out 9 baskets out of 30. Since this is our proportion( 9:30 ), we can simplify it which brings us to 3:10. And since we must find how much he will take out in 50 tries, We multiply the proportion by 5 which is 15:50, meaning he will make 15 baskets.

Final answer:

Cameron can make 15 baskets out of 50 attempts based on his success rate, which is half of his sister Annie's success rate of 60%.

Explanation:

Annie can make 18 baskets out of 30 attempts, which means her success rate is 60% (since 18 is 60% of 30). Her younger brother Cameron can make half as many baskets in the same number of attempts, so Cameron's success rate is 30% because half of 18 is 9, and 9 is 30% of 30. If Cameron were to attempt 50 shots, we would calculate the number of baskets he can make by applying his success rate to these 50 attempts. Therefore, 30% of 50 is 15. This means Cameron can make 15 baskets out of 50 attempts.

Answer:

A) 2(6x + 13)

Step-by-step explanation:

2(5 + 8 + 6x)

= 2(13 + 6x)

= 2(6x + 13)

Answer:

2(6x + 13)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Factor out 6

I assume you mean 6x^2+30x+36, because that makes far more sense

6(x^2+5x+6) = 6(x^2 + 2x +3x +6)

(To find that it is 2x and 3x: 2 +3 = 5, 2 * 3 = 6)

Factor by grouping:

6* x(x+2) +3(x+2) = 6(x+3)(x+2)

For binomials, it could be either (6x+18) (x+2) or (x+3) (6x+12), depending on where you multiply the 6.

Answer:x+2

Step-by-step explanation:

Answer:

-4r

Step-by-step explanation:

r + (-5r)

1r + (-5r)

Factor out an r

r( 1 -5)

One minus 5 is negative 4.   If you have one dollar and you borrow five dollars,  how much did you borrow?  4  but that 4 is borrowed so it is negative

r (-4)

-4r

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

[tex]\sin \angle OTR=\frac{r/2}{r}=\frac{1}{2}\implies \angle OTR =\frac{\pi}{6}[/tex]

and since <TRO=pi/2, it must be that

[tex]\angle TOR =\pi-\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}[/tex]

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

[tex]\angle SOT = \pi - \angle TOR = \pi - \frac{\pi}{3} = \frac{2}{3}\pi[/tex]

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can  determine angle <OTS:

[tex]\angle OTR \cong \angle PTR=\frac{\pi}{6}\implies\angle OTS=\angle PTS -\angle PTR -\angle OTR\\\angle OTS = \frac{\pi}{2}-\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{6}[/tex]

and so the angle <OST is

[tex]\angle OST = \pi - \angle TOS - \angle OTS = \pi -\frac{2}{3}\pi - \frac{1}{6}\pi=\frac{\pi}{6}[/tex]

Towards determining |TS|:

Use cosine:

[tex]\cos \angle OST =\frac{|RS|}{|ST|}\implies |ST|=\frac{\frac{3}{2}r}{\cos \frac{\pi}{6}}=\frac{12\cdot 2}{\sqrt{3}}=8\sqrt{3}cm[/tex]

Finally, we can determine the arc length QT:

[tex]QT = {\angle OST}\cdot |ST|=\frac{\pi}{6}\cdot 8 \sqrt{3}=\frac{4\pi}{\sqrt{3}}\approx 7.255cm[/tex]

3=x/100*12

x/25*3=3

x=3:3/25

x=25

The answer is 25%. Hope this helps! <3

Answer:

3 is 25% of 12

Step-by-step explanation:

Slope-intercept form:

y = mx + b   "m" is the slope, "b" is the y-intercept

For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -3/4

perpendicular line's slope is 4/3

#1: The slopes are the same, meaning they are parallel lines

#2: First isolate the "y" in the first equation

-4x + 5y = -5

5y = -5 + 4x

y = -1 + 4/5x   They are not perpendicular because the slopes are 4/5 and -4/5

#3: Isolate "y" in the second equation

8y = 3x - 32

y = 3/8x - 4         They are perpendicular

#4: Isolate "y" is the 1st equation

10y = -9x

y = -9/10x     They are parallel lines

The 3rd choice is your answer

Answer:

slope = - [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

note that BC is perpendicular to AB, hence the slope of BC is the negative reciprocal of the slope of AB

[tex]m_{BC}[/tex] = - [tex]\frac{1}{2/3}[/tex] = - [tex]\frac{3}{2}[/tex]

The answer is George Washington.

Answer:

The first president was George Washington. Hope this helps you out.

Step-by-step explanation:

Answer:

Correct answer is C.

Step-by-step explanation:

Note that graph in the diagram has period [tex]\pi.[/tex]

Consider the function [tex]y=-2\cos (2(x+\pi ))-1.[/tex]

This function has a period [tex]T=\dfrac{2\pi}{2}=\pi.[/tex] Functions in another options have period that differes from [tex]\pi.[/tex]

The graph of this function passes through the point (0,-3), because

[tex]y(0)=-2\cos (2(0+\pi ))-1=-2\cos 2\pi-1=-2\cdot 1-1=-3.[/tex]

Answer:

[tex]y=-2cos (2(x+\pi ))-1[/tex]

Step-by-step explanation:

We are a given a graph from which we can clearly see that y = -1 when x  = 0.

Next, we will find out which of the options is the equation of the given graph and for that we need to set our calculator to the radian mode and then put the value of x to be 0.

1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1  = 3

2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1

3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3

We get y = -1 when x = 0 in equation number 3, y = -2 cos (2(x + pi)) - 1, so that is the equation of the given graph.

Answer:

y^2 +8y + 16

Step-by-step explanation:

 6y^2 +2y +5  - (5y^2 -6y -11)

I distribute the minus sign

6y^2 +2y +5  - 5y^2 +6y +11

Then I put them vertical.

6y^2 +2y +5  

-5y^2 +6y +11

------------------------

y^2 +8y + 16

This is in standard from since the exponential decreases.

Answer:

[tex]4x^2+34x-28=0[/tex]

x = 0.76

Step-by-step explanation:

We can write the area of steel before it is cut as:

Area = [tex](11+2x)*(6+2x)cm^2[/tex]

Expanding it by multiplying the brackets to get:

Area = [tex]4x^2+22x+12x+66[/tex]

Area  area of steel before cutting = [tex]4x^2+34x+66[/tex]

Then we need the area of steel after 11*6 inside dimensions are cut out:

[tex]4x^2+34x+66-(11*6)=4x^2+34x[/tex]

This area should be close to 28 cm[tex]^2[/tex], hence the equation becomes:

[tex]4x^2+34x-28=0[/tex]

Moreover, plotting the graph gives us a value of x = 0.76.

Answer:

Step-by-step explanation:

4x2+34x-28

0.76cm

plato

Answer:

295.16 feet

Step-by-step explanation:

We need to find the length of the diagonal of a right angled triangle with equal length legs.

Length of each leg = √(43560)

Using the Pythagoras theorem:-

x^2 = (√(43560))^2 + (√(43560))^2    (where x = length of the diagonal)

x^2 = 43560 + 43560

x = √(87120) = 295.16 feet

Answer:

distance from corner to corner = 295.16 ft

Step-by-step explanation:

Given the land is square, then its area is computed as:

Area = (length of a side)^2

Replacing with area = 1 acre =  43560 sq. ft.

43560 = (length of a side)^2

length of a side = √43560

length of a side = 208.71 ft

The distance from corner to corner and two sides of the square form a right triangle, where the distance from corner to corner is the hypotenuse and the square sides are the legs. From Pythagorean theorem:

(distance from corner to corner)^2 = 208.71^2 + 208.71^2

distance from corner to corner = √(208.71^2 + 208.71^2)

distance from corner to corner = 295.16 ft

Answer:

The difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].

Step-by-step explanation:

The given expression is

[tex]\frac{2x+5}{x^2-3x}-\frac{3x+5}{x^3-9x}-\frac{x+1}{x^2-9}[/tex]

Find factors of denominators.

[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x^2-9)}-\frac{x+1}{x^2-9}[/tex]

Use [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x-3)(x+3)}-\frac{x+1}{(x-3)(x+3)}[/tex]

Take  [tex]x(x+3)(x-3)[/tex] as LCD.

[tex]\frac{(x+3)(2x+5)-(3x+5)-x(x+1)}{x(x+3)(x-3)}[/tex]

[tex]\frac{(2x^2+5x+6x+15)-3x-5-x^2-x}{x(x^2-3^2)}[/tex]

[tex]\frac{2x^2+5x+6x+15-4x-5-x^2}{x(x^2-9)}[/tex]

[tex]\frac{x^2+7x+10}{x^3-9x}[/tex]

Therefore the difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].

Answer:

(x+5)(x+2)/x^3-9x

Step-by-step explanation:

For short if taking on edgen then option A is correct.

Answer:

1: 6

2: 1,2,3

3: 4m-1>5m-4

4: Not enough data

5: n = 11

6: The ceiling is lower than 3m

7: G = 7

8: C = 18

9: p + 18 = 41; p = 23

10: D = 100t

Step-by-step explanation:

Question 1:

5*2+x/2-7

5*2+6/2-7

10+6/2-7

10+3-7

13-7

6

Question 2:

4*2<16

8<16 True

4*1<16

4<16 True

4*3<16

12<16 True

4*4<16

16<16 False

Question 3:

Let's plug in 1 for m

4*1-1____5*1-4

4-1_____5-4

3_____1

3>1

Question 4:

You did not give an equation, so I cannot answer.

Question 5:

2*11 + 5 =27

22 + 5 = 27

27 = 27

So n = 11

Question 6:

x<3

The ceiling is lower than 3m because x<3

Question 7:

5.1g = 35.7

5.1g/5.1=35.7/5.1

g = 7

Check: 5.1 * 7 = 35.7

Question 8:

36 + c = 54

36 + c -36 = 54 - 36

c = 18

Check: 36 + 18 = 54

Question 9:

p + 18 = 41; p = 23 is correct because the number of paperback books plus the number of hardcover books would equal the total number of books sold. Check: 23 + 18 = 41

Question 10:

d=100t is correct because each time t goes up one it goes up 100. Example: if it is at one hour, than it is 100, if it is at 3 hours, than d = 100*3 = 300, which is the same pattern as the table.

Hope this helps!

The expression 5x² + x - 7 is calculated by substituting x with 6. Inequality and equation solving techniques are used to find the solutions to 4n < 16, 4m - 1 compared to 5m - 4, and other given problems, resulting in specific numerical solutions and identifying suitable real-world scenarios like a ceiling height represented by x < 3.

To solve the expression 5x² + x
- 7 where x equals 6, we substitute and get 5(3)² + (3) - 7 = 45 + 3 - 7 = 41.

The solutions to the inequality 4n < 16 from the set {1,2,3,4} are 1, 2, and 3, since 4 times each of these is less than 16.

Comparing the expressions when m = 3, we get 4m - 1 and 5m - 4. Substituting we have 12 - 1 < 15 - 4, thus 11 < 11, which is false, so 4m - 1 = 5m - 4.

The inequality 15 > w is only true for w = 14. Values w = 15 and w = 21 do not satisfy the inequality.

In the equation 2n + 5 = 27, solving for n within the replacement set gives n = 11 as the correct solution.

The inequality x < 3 represents a situation where The ceiling is lower than 3 m.

To solve 5.1g = 35.7, divide both sides by 5.1 to find g = 7.

For the equation 36 + c = 54, subtract 36 from both sides to get c = 18.

Cassandra's situation is best represented by the equation p + 18 = 41, resulting in p = 23 paperback books sold.

The relationship between the distance d and time t from the truck table is d = 100t, since distance is increasing by 100 kilometers every hour.

Answer:

x=3

Step-by-step explanation:

Basically the question is asking what value of x gives the same value for y

(or where do the 2 lines cross)

the input is x=3, the out put is y =-1

Answer:

x = 3

Step-by-step explanation:

X - LINE: Horizontal

Y - LINE: VERTICAL

The reason why it's x = 3 is because it's where both line up to, where they both intersect.

Input (x) is 3 & output (y) is -1

Hope this helps you!!! :)

Answer:

EACH TIE COSTS 7.43

Step-by-step explanation:

If 13.35x13=173.55 then that means the ties total is 189.46 now devide that by 22 it equals 13.35

The cost calculation of a tie can be done by subtracting the total cost of the shirts from the total cost. The remainder is then divided by the number of ties bought, resulting in the price of a tie, about $7.43.

To find the cost of a tie, we'll first determine the total cost of the shirts and then subtract this from the total spent. Firstly, we need to calculate the total cost of the shirts by multiplying the cost of one shirt by the number of shirts purchased. That is 13 shirts * $15.35/shirt = $199.55.

Next, we subtract the total cost of the shirts from the total spent to find out how much was spent on ties: $363.01 (total spent) - $199.55 (total spent on shirts) = $163.46 (total spent on ties).

Now, to find the cost of one tie, we divide the total spent on ties by the number of ties purchased. That is: $163.46/22 ties = $7.43/tie. Therefore, each tie costs approximately $7.43.

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Answer:

let x be the Robert piece

y Maria's piece

x+y=10

0,5*x ( half of Robert piece)= 2/3 y( 2 thirds)

2 equations then

x+y= 10 then x= 10-y

0,5x= 0,67 y  then we replace x by 10-y on the second equation and it gives

0,5(10-y)= 5-0,5y=0,67y

5= 1,17 y so y= 4,27    and then x= 10-y= 5,73

the question asks how much Robert wire is longer than Maria's wire

so we get x-y= 1,46

Robert's wire is longer [tex]\frac{4}{3}[/tex] times than Maria's wire and also   it [tex]\frac{10}{7}[/tex] longer than Maria's wire

A wire is a single, usually cylindrical, flexible strand or rod of metal. It are used to bear mechanical loads or electricity and telecommunications signals.  

Half of Robert's wire = 2 thirds of Maria's wire, so

[tex]\frac{1}{2} *[/tex]  Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]

The total length of their wires = 10 feet

10 feet =  Robert's wire + Maria's wire

10 feet =  [tex]\frac{4}{3} * Maria's wire[/tex] + Maria's wire

10 feet =  [tex]\frac{7}{3} * Maria's wire[/tex]

Maria's wire =  [tex]\frac{30}{7}[/tex]  feet

 [tex]\frac{1}{2} *[/tex]   Robert's wire = [tex]\frac{2}{3} * Maria's wire[/tex]

Robert's wire = [tex]\frac{4}{3} * \frac{30}{7} [/tex]

Robert's wire =  [tex]\frac{120}{21} feet[/tex]

Robert's wire = [tex] \frac{40}{7} feet[/tex]

If we draw the piece, we get the information that

7 units = 10 feet

1 unit = [tex]\frac{10}{7}[/tex] feet

Hence the  Robert's wire is [tex]\frac{10}{7}[/tex] longer than Maria's wire because

Robert's wire - Maria's wire =   [tex]\frac{40}{7} - \frac{30}{7} feet = \frac{10}{7} feet[/tex]

Grade:  5

Subject:  math

Chapter:  wire

Keywords:  

wire, feet,  piece of wire, piece, wires

Final Answer:

The difference in the unit price per ounce for the laundry detergent Mr. and Mrs. O’Brien purchased is $0.045 per ounce, with Mr. O’Brien's detergent being the more cost-effective option.

Explanation:

To find the unit price per ounce for each type of laundry detergent, we first determine the cost per ounce by dividing the total cost by the total weight. For Mrs. O’Brien's detergent, which is 112 ounces for $13.44, the unit price per ounce is $13.44/112 = $0.12 per ounce. For Mr. O’Brien's detergent, which is 17.5 pounds for $19.60, we convert pounds to ounces (1 pound = 16 ounces) and calculate the unit price per ounce as $19.60/(17.5 * 16) = $0.165 per ounce.

The difference in unit price per ounce is then found by subtracting Mrs. O’Brien's unit price from Mr. O’Brien's unit price, resulting in $0.165 - $0.12 = $0.045 per ounce. The positive value indicates that Mr. O’Brien's detergent is more cost-effective on a per-ounce basis.

This mathematical approach provides a clear comparison of the unit prices, allowing consumers to make informed decisions based on cost-effectiveness. The calculated difference highlights the savings per ounce associated with Mr. O’Brien's laundry detergent.

Answer:

$0.13 (this is a rounded answer)

Step-by-step explanation:

The unit cost is the cost of a 1 ounce bottle so you would divide the cost by the total number of ounces:

$2.00 divided by 16 is 0.125 but you would round because you need a cost not a decimal.

So your final answer would be $0.13 per ounce.

Answer:

$.13 per fl oz

Step-by-step explanation:

To find the unit cost, we take the cost and divide by the number of units

$2.00/16

$.125 per fl oz

Since this is money we round to the nearest cent.

$.13 per fl oz

Answer:

10 is 5,650

9 is 18.5

11 is 71.24

Step-by-step explanation:

11 .2.74  x25

Answer:

x = -2, y = 0

Step-by-step explanation:

This is a systems of equations. Using substitution, we solve for a single variable, plug it in to solve for the other, and solve that one back in to solve for the original. Let's solve it.

5x + y = -10

Subtract 5x from both sides.

y = -5x - 10

Now that we have y isolated, we can plug it in to the other equation.

4x - 7(-5x-10) = -8

Distribute.

4x + 35x + 70 = -8

Subtract 70 from both sides and simplify.

39x = -78

Divide both sides by 39.

x = -2

Now that we have x as -2, we plug it in to the original.

5(-2) + y = -10

Simplify.

-10 + y = -10

Add 10 to both sides.

y = 0

x = -2, y = 0

[tex]\left\{\begin{array}{ccc}5x+y=-10&|\text{subtract 5x from both sides}\\4x-7y=-8\end{array}\right\\\left\{\begin{array}{ccc}y=-5x-10&|\text{substitute to the second equation}\\4x-7y=-8\end{array}\right\\\\4x-7(-5x-10)=-8\qquad\text{use distributive property}\\\\4x+(-7)(-5x)+(-7)(-10)=-8\\\\4x+35x+70=-8\qquad\text{subtract 70 from both sides}\\\\39x=-78\qquad\text{divide both sides by 39}\\\\\boxed{x=-2}\\\\\text{Put the value of x to the first equation}\\\\y=-5(-2)-10\\\\y=10-10\\\\\boxed{y=0}[/tex]

[tex]Answer:\ \boxed{x=-2\ and\ y=0}[/tex]