Factoring Trinomials (
Factor each completely.
1) 3p² – 2p - 5

Answer:

0, 5, 7, 11, ...

Step-by-step explanation:

1^2 = 1; 1 - 1 = 0; 0 is divisible by 6

5^2 = 25; 25 - 1 = 24; 24 is divisible by 6

7^2 = 49; 49 - 1 = 48; 48 is divisible by 6

11^2 = 121; 121 - 1 = 120; 120 is divisible by 6

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

5x + y = 21 → (1)

x - 3y = 9 → (2)

Multiply (1) by 3 and add the result to (2) to eliminate y term

15x + 3y = 63 → (3)

Add (2) and (3) term by term

(x + 15x) + )- 3y + 3y) = (9 + 63)

16x = 72 ( divide both sides by 16 )

x = 4.5

Substitute x = 4.5 into (1) for corresponding value of y

22.5 + y = 21 ( subtract 22.5 from both sides )

y = - 1.5

Solution is (4.5, - 1.5 )

The median number of laptop computers sold per month is 15, calculated by arranging the sales data in ascending order and averaging the two middle values in the even-numbered dataset.

The median of laptop computers sold per month can be calculated by first arranging the given numbers in ascending order and then finding the middle value. If there is an even number of observations, the median is the average of the two middle numbers.

Answer:

Answer:3.33

Answer:3.33 Step-by-step explanation:

The answer is 3.33

2/3 × 5 = 3.33

Answer:

Step-by-step explanation:

2/3 × 5 = 10/3

Answer:

2y=-5x

Step-by-step explanation:

First you mark your terms, which means to basically put the equation in order.

Then you add, for instance, first you'll add y and 1, you'll have 2y because y means one. Then, you'll have -2 minus 3 and you'll get -5 then you carry on the variables to the solutions.

Answer:

2y=-5x

hope this helps :3

Answer:

5(V + 48) = 290

Step-by-step explanation:

5 times the sum of V and 48 is 290:     V + 48

5 times the sum of V and 48 is 290:     5(V + 48)

5 times the sum of V and 48 is 290:     5(V + 48) = 290

Answer:

8cm

Step-by-step explanation:

Ab=7cm

Since opposite sides are equal

Cd=7cm

7cm + 7cm = 14cm

Perimeter equals 30cm

:.30cm - 14cm =16cm (bc+ad)

Since both bc and ad are equal,

16cm/2=8cm

:.ad=8cm

Final answer:

In a parallelogram, opposite sides are equal, so by using the given perimeter of 30 cm and one side of 7 cm, we find the length of the adjacent side AD to be 8 cm.

Explanation:

In the given problem with parallelogram ABCD, we know AB = 7 cm and the perimeter is 30 cm. In a parallelogram, opposite sides are equal in length, so if AB = 7 cm, then CD also equals 7 cm. The perimeter P of a parallelogram is the sum of all its sides:

P = AB + BC + CD + DA

Given P = 30 cm and AB = CD = 7 cm, we can find the length of AD (which is also equal to BC) using the formula:

P = 2(AB + AD)

30 = 2(7 + AD)

30 = 14 + 2(AD)

30 - 14 = 2(AD)

16 = 2(AD)

AD = 16 / 2 = 8 cm

Therefore, the length of AD is 8 cm.

Answer:

yes.

Step-by-step explanation:

24/48 is half. Anything less than 24 would be less than half.

Answer:

Yes.

Step-by-step explanation:

Half of 2 is 1, so 1/2 means half.

Half of 48 is 24, so 24/48 is also half.

23/48 is less than 24/48, so 23/48 is less than 1/2.

Answer:

hello : a²b² =4

Step-by-step explanation:

2ײ + 3x - 4=0

The roots of this equation exist because (2)(-4)<0

note : a'x²+b'x +c' =0.......The roots of this equation : a and b

a×b = c'/a'       a' =2 and b'=3 and c' = - 4

in this exercice ; a²b² = (ab)² = (c'/a')²  = (-4/2)² = (-2)² =4

Answer:

4

Step-by-step explanation:

given a quadratic equation in standard form

y = ax² + bx + c = 0 : a ≠ 0

with roots α and β, then

the sum of the roots α + β = - [tex]\frac{b}{a}[/tex] and

the product of the roots αβ = [tex]\frac{c}{a}[/tex]

2x² + 3x - 4 = 0 ← is in standard form

with a = 2, b = 3 and c = - 4

αβ = [tex]\frac{-4}{2}[/tex] = - 2, hence

α²β² = (αβ)² = (- 2)² = 4

Answer:

80 kg is Hamid's normal weight

Step-by-step explanation:

The following equation will help you to find the answer:

(1.10)x = 88

Answer:79.2kg

Step-by-step explanation:

10%of 88kg is 8.8. Subtract 8.8 from 88 and the answer is 79.2.

Answer:

675 miles

Step-by-step explanation:

7.5*90 (for the 1 1/2 hour)

Answer:

1 1/2= 90 minutes

90 minutes/7.5 miles per minute

Multiply

90/7.5

= 675 miles in 1 1/2

Hope this helped :)

Answer: 16 cm^2.

Step-by-step explanation: The volume of a pyramid is equal to one-third the product of the area of the base and the height:

[tex]V=\frac{1}{3}A*h[/tex]

In this case, the base is a square, so its area is:

A=L^2 where "L" is the lenght of the base edge

So the volume would be:

[tex]V=\frac{1}{3}L^{2} *h[/tex]

[tex]V=\frac{1}{3}4^{2} *3[/tex]

V=16*3/3

[tex]V=16cm^{2}[/tex]

Final answer:

The solution to the inequality -x > 4 is all real numbers less than -4, which can be expressed as the interval (-∞, -4). This is found by dividing both sides by -1 and reversing the inequality to x < -4.

Explanation:

When considering the inequality -x > 4, we are trying to find the set of all values for the variable x that make the inequality true. The solution to such an inequality requires inverse operations and understanding the rules for inequalities, especially the rule that multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.

Step by step, let's solve the given inequality:

This means that any number lower than -4 will be a valid solution for the inequality -x > 4. It's also valuable to visualize this set on a number line, where everything to the left of -4 (but not including -4 itself) is part of the solution set.

Hello There!

1[tex]\frac{3}{4}[/tex] + 2[tex]\frac{3}{8}[/tex] = 4[tex]\frac{1}{8}[/tex]

First, when we are trying to find the sum of a mixed number, I always add the natural numbers first meaning that the numbers before the fraction so I would add 1 and 2 together so we get a sum of 3 and now we are left with just a plain fraction.

Next, I find the least common denominator which is the smallest number that can be a common denominator for a set of fractions. Our lowest common denominator is 8 because [tex]\frac{3}{4}[/tex] = [tex]\frac{6}{8}[/tex].

Then, we add our fractions with the denominator of 8 together and get a sum of 9/8 which we can turn into a mixed number because the numerator is bigger than our denominator.

Our mixed number turns into 1 and 1/8 and we add 4 to it because that was the sum of our natural numbers and get a sum of 4 and 1/8

ANSWER 4 1/8

Answer: 4

Step-by-step explanation: To have an equation with no solution you have to get something like 0=1 meaning you have to remove all the variables. In this equation you would distribute to get xy+2y+2x=2x+12+4x where y is the missing number. then combining like terms you get xy+2x+2y=6x+12. Subtracting 2x from both sides you get xy+2y=4x+12. Now to get the variables gone y has to be 4 so that the variables to cancel out. By plugging in 4 you can see this works; 4x+8=4x+12 and by subtracting 4x from both sides you get 8=12 which is not true meaning there is no solution.

ANSWER

[tex]^{\boxed {}} = 4.[/tex]

EXPLANATION.

The given equation is

[tex] \boxed {}(x + 2) + 2x = 2(x + 6) + 4x[/tex]

Let us expand the right hand side to obtain:

[tex]\boxed {}(x + 2) + 2x = 2x + 12+ 4x[/tex]

We group similar terms and keep the expression with the box on the left.

[tex]\boxed {}(x + 2) = 2x - 2x+ 12+ 4x[/tex]

Simplify

[tex]\boxed {}(x + 2) = 4x + 12[/tex]

We can see that the value of box the will be the equation to have no solution is 4.

Let us substitute 4 for box.

[tex]4(x + 2) = 4x + 12[/tex]

[tex]4x + 8 = 4x + 12[/tex]

[tex]4x - 4x = 12 - 8[/tex]

[tex]0 = 4[/tex]

This is not true. Hence the equation has no solution when

[tex]\boxed {} = 4[/tex]

Answer:

The answer is....

Step-by-step explanation:

y= -10x+400

Follow below steps:

The student's question involves writing a linear function for the height of an elevator as a function of time, given that the elevator descends from 400 feet to 250 feet in 15 seconds.

First, let's find the rate of descent by calculating the change in height over the change in time. This gives us (250 feet - 400 feet) / (15 seconds) = -10 feet per second. The negative sign indicates a downward movement.

Now, we can construct the linear function for height h(t), where t is the time in seconds. The initial height is 400 feet, so the y-intercept of our linear equation is 400. With a slope of -10, the function takes the form:

h(t) = -10t + 400

This function represents the height of the elevator after t seconds.

Answer:

3/5

Step-by-step explanation:

cos A = [tex]\frac{AC}{AB}[/tex]=[tex]\frac{9}{15}[/tex]=[tex]\frac{3}{5}[/tex]

Answer:

Cos A = 3/5

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

From the figure we can see a right angled triangle, ABC

AC = 9, CB = 12 and AB = 15

To find the value of Cos A

Cos A = Adjacent side/Hypotenuse

 = AC/AB

 = 9/15  = 3/5

Therefore the value of Cos A = 3/5

Step-by-step explanation:

-52-1x= 9(x+9)+9x

-52-1x= 9x+81+9x (now combine like terms)

-52-1x= 18x+81

-1x= 18x+81

            -52

-1x=18x+29

-1x=29

+18x

17x= 29

      ÷17

x=1.705

Hope this helps, I'm not good at explaining it with words, so I just showed the work...

The height of the tree is 32 feet.

Step-by-step explanation:

Let the height of the tree be x.

Connect the top of the tree, the point on the ground, and the bottom of the tree to form a right triangle.

Use Pythagorean theorem to solve for x.

(4+2x)^2 = x^2 + 60^2

x = 32

The height of the tree is 4 feet.

To find the height of the tree, we can set up a right triangle with the tree height as one leg, the distance from the base of the tree as the other leg, and the distance to the top of the tree as the hypotenuse. Let's call the tree height x. From the given information, we can write the equation:

x = 2x + 4

Simplifying this equation, we get:

x = 4

Therefore, the height of the tree is 4 feet.

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Answer: d

Step-by-step explanation:

The true statement is a smaller percentage of second-lunch students (38%) eat outside.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.

Percentage of the second lunch students that eat outside = (0.21/0.55) x 100 = 38%

To learn more about percentages, please check: https://brainly.com/question/25764815

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Answer:

x y^2 (11 x y - 4)

Step-by-step explanation:

Simplify the following:

4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)

Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:

4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)

-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:

4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3

Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):

(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)

x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:

11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)

x y^2 2 + x y^2 (-6) = -4 x y^2:

11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)

2 y - 2 y = 0:

11 x^2 y^3 - 4 x y^2

Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:

Answer:  x y^2 (11 x y - 4)

Answer:  xy2 • (11xy - 4)

Step-by-step explanation:

4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)

Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:

4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)

-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:

4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3

Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):

(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)

x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:

11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)

x y^2 2 + x y^2 (-6) = -4 x y^2:

11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)

2 y - 2 y = 0:

11 x^2 y^3 - 4 x y^2

Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:

Answer:  x y^2 (11 x y - 4)

Answer:

7/4, 1.25 or 1 3/4

Step-by-step explanation:

Answer:

Exact form  7/4

Decimal form 1.75

Mixed Number 1 3/4

Step-by-step explanation:

Answer:

The answer is 30

Step-by-step explanation:

BC the inside of a triangle equals 180

Answer: [tex]x^{\frac{2}{3} }[/tex]

Step-by-step explanation:

We have several properties of exponents in use here. The two that are used are:

[tex](x^{a})(x^{b}) = x^{a + b}[/tex] (Exponents with the same base that are being multiplied together can have the exponents added)

[tex](x^{a})^{b} = x^{(a)(b)}[/tex] (A base raised to a power, and then raised to another power means that you can multiply the exponents to get the same result as doing inside operations and then outside operations)

Let's apply it!

First, let's simplify what's inside the parenthesis.

[tex]x^{\frac{4}{3} } x^{\frac{2}{3} }[/tex] (Remember, they have the same base of "x", so we can add the exponents)

[tex]x^{\frac{4}{3} + \frac{2}{3} }[/tex] = [tex]x^{\frac{6}{3} }[/tex] = [tex]x^{2}[/tex]

Now we have [tex](x^{2})^{\frac{1}{3} }[/tex]. Let's use the second rule.

[tex](x^{2})^{\frac{1}{3} }[/tex] = [tex]x^{\frac{2}{3} }[/tex]

Hope this helps! :^)

Answer:

B

Step-by-step explanation:

Just took the test

Answer:

$2389.14

Step-by-step explanation:

The equation is I = PRT

330= (0.0425)(3.25)P

P=2389.14

Answer:

$2389.14.

Step-by-step explanation:

Use the formula

I =  PRT/100 where I = interest , P  is the principle, t = time and R = the rate.

330 = P * 4.25 * 3.25 / 100

33000 = P * 13.8125

P = 33,000 / 13.8125

P = $2389.14.

Answer:

If it is sediment: A sediment trap is a T-shaped pipe configuration designed to catch any debris in a gas line before it goes into the appliance.

Or if it was a typo and its supposed to say segment:line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

Step-by-step explanation:

I know this because of the help of google.

Answer:

Option C [tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]

Step-by-step explanation:

we have that

The given equation is

[tex]-16p+37=49-21p[/tex]

Solve for p

Group terms that contain the same variable

[tex]-16p+21p=49-37[/tex]

Combine like terms

[tex]5p=12[/tex]

[tex]p=12/5[/tex]

[tex]p=2.4[/tex]

we know that

If a equation has the same solution as the given equation, then the solution of the given equation must satisfy the equation

Verify each case

case A) we have

[tex]2+1.25p=-3.75p+10[/tex]

substitute the value of p=2.4 in the equation and then compare the results

[tex]2+1.25(2.4)=-3.75(2.4)+10[/tex]

[tex]5=1[/tex] ----> is not true

therefore

The equation does not have the same solution as the given equation

case B) we have

[tex]-55+12p=5p+16[/tex]

substitute the value of p=2.4 in the equation and then compare the results

[tex]-55+12(2.4)=5(2.4)+16[/tex]

[tex]-26.2=28[/tex] ----> is not true

therefore

The equation does not have the same solution as the given equation

case C) we have

[tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]

substitute the value of p=2.4 in the equation and then compare the results

[tex](3/2)(2.4)-5+(9/4)(2.4)=7-(5/4)(2.4)[/tex]

[tex]4=4[/tex] ----> is true

therefore

The equation has the same solution as the given equation

case D) we have

[tex]-14+6p=-9-6p[/tex]

substitute the value of p=2.4 in the equation and then compare the results

[tex]-14+6(2.4)=-9-6(2.4)[/tex]

[tex]0.4=-5.4[/tex] ----> is not true

therefore

The equation does not have the same solution as the given equation

Answer:

[tex] \frac{11}{12} [/tex]

The quotient in lowest terms is 2.

The quotient step by step for the given expression:

1. Given Expression:

[tex]\[ \frac{3}{\frac{2}{4}} : 3 \][/tex]

2. Step 1: Simplify the Complex Fraction:

  - The complex fraction is [tex]\( \frac{3}{\frac{2}{4}} \).[/tex]

  - To simplify, multiply the numerator by the reciprocal of the denominator:

[tex]\[ \frac{3}{\frac{2}{4}} = 3 \times \frac{4}{2} = 6 \][/tex]

3. Step 2: Divide by 3:

  - Now divide the simplified fraction (6) by 3:

[tex]\[ 6 : 3 = 2 \][/tex]

Therefore, the quotient in lowest terms is 2.

Answer:

.30p

Step-by-step explanation:

Answer:  C) (2,0), (-4,-8), (-2, 1)

Step-by-step explanation:

The translation rule for translating a point (x,y) by k units down :-

[tex](x,y)\rightarrow(x,y-h)[/tex]

Given :   A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down.

Then, its new coordinates will be :

[tex](2,3)\rightarrow(2,3-3)=(2,0)[/tex]

[tex](-4,-5)\rightarrow(-4,-5-3)=(-4,-8)[/tex]

[tex](-2, 4)\rightarrow(-2,4-3)=(-2,1)[/tex]

Hence, the new coordinates =  (2,0), (-4,-8), (-2, 1)