Use the zero product property to find the solutions to the equation 2x2 + x - 1 = 2

a) x= -1/2 or x =2
b) x= -2 or x =1/2
c) x= -3/2 or x =1
d) x= 1 or x= 3/2​

Answer:  39) 1              40) 2

                41) 1              42) 0

Step-by-step explanation:

39)     ∠A = ?        ∠B = ?       ∠C = 129°

            a = ?          b = 15         c = 45

Use Law of Sines to find ∠B:

[tex]\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o[/tex]

If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°

If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°

Since ∠A cannot be negative then ∠B ≠ 165°

∠A = 36°        ∠B = 15°       ∠C = 129°       is the only valid solution.

40)      ∠A = 16°        ∠B = ?       ∠C = ?

             a = 15           b = ?         c = 19

Use Law of Sines to find ∠C:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o[/tex]

If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°

If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°

Both result with ∠B as a positive number so both are valid solutions.

Solution 1:  ∠A = 16°        ∠B = 144°       ∠C = 20°    

Solution 2:  ∠A = 16°        ∠B = 4°       ∠C = 160°    

41)       ∠A = ?        ∠B = 75°       ∠C = ?

             a = 7           b = 30         c = ?

Use Law of Sines to find ∠A:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o[/tex]

If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°

If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°

Since ∠C cannot be negative then ∠A ≠ 167°

∠A = 13°        ∠B = 75°       ∠C = 92°       is the only valid solution.

42)      ∠A = ?         ∠B = 119°       ∠C = ?

             a = 34         b = 34           c = ?

Use Law of Sines to find ∠A:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o[/tex]

If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°

If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°

Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°

There are no valid solutions.

CHECK THE COMPLETE QUESTION BELOW;

Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza with t toppings, her total cost can be found using this expression: 0.90(2.25d + 1.40t + 6). What is the total cost for Lindy and her friends to order 4 drinks and a medium pizza with 3 toppings? A. $17.28 B. $16.52 C. $15.69 D. $28.40

Answer:

OPTION A. is correct

A)$17.28

Step-by-step explanation:

From the question we were giventhis expression as the total cost for all.

0.90(2.25d + 1.40t + 6).

We know that Lindy and her friends to order 4 drinks and a medium pizza with 3 topping

Then we can say d= 4 and t= 3 ,

Then we can substitute into below expresion

0.90(2.25d + 1.40t + 6).

0.90[2.25(4)+1.40(3)+6]

= 0.90[9+4.2+6]

= 17.8

Hence the total cost for Lindy = $ 17.28

Answer:

see attached diagram

Step-by-step explanation:

1.  1 and 70 are angles on a line (supplementary)

2. vertical angles with 70

3. angles on a line are supplementary

4. 2 and 4 are supplementary interior angles between parallel lines m & n

5. corresponding angle with 70

Answer:

210 students

Step-by-step explanation:

The total number of students surveyed was

19+14+30+23+14 = 100

The fraction that picked Yosemite is 14/100

Multiply that fraction by the total number of students

1500* 14/100 = 210

Answer:

210 students

Step-by-step explanation:

vote me brainliest plz

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

Attached below....

Number form:820,245

Word form: eight hundred twenty thousand two hundred forty-five

Expanded form: 800,000+20,000+0+200+40+ 5

Place value chart below!!

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

11 and 2/3.

Step-by-step explanation:

6 and 3/12 = 72/12 + 3/12 = 75/12.

5 and 5/12 = 60/12 + 5/12 = 65/12.

75/12 + 65/12 = 140 / 12 = 70 / 6 = 35 / 3 = 11 and 2/3.

Hope this helps!

Answer: 11 2/3

Step-by-step explanation:

[tex]6\frac{3}{12}+5\frac{5}{12}[/tex]

[tex]Add\:whole\:numbers[/tex]

[tex]6+5=11[/tex]

[tex]Combine\:fractions[/tex]

[tex]\frac{3}{12}+\frac{5}{12}=\frac{8}{12}[/tex]

[tex]Simplify[/tex]

[tex]\frac{8}{12} =\frac{2}{3}[/tex]

[tex]11+\frac{2}{3}[/tex]

[tex]=11\frac{2}{3}[/tex]

Answer:

k=180-23-90=67...................

Answer:

< k = 67°

Step-by-step explanation:

HJ tangent to HG => < H = 90°

< K = 180° - (<J + <H)

= 180° - (90° + 23°)

= 180° - 113°

= 67°

Answer:

Step-by-step explanation:

width of a rectangle=11 cm=11*5=55 ft

length of  rectangle =8 cm= 8*5=40

Area=55*40=2220 ft²

height=3 cm=3*5=15

base=11 cm=11*5=55

Area of a triangle=base*height/2=15*55/2= ft^2

2220+412.5=2632.5 ft^2

this number is close to 2615 if the square unit on the grid =1 cm

Answer:

I won't give you the answer straight away so you take the time to read my answer and understand

Step-by-step explanation:

We knoe that 2 to the third is 8. when you square to a negative power, you do squaring normally, and then take the reciprocal of that number. so 8 to the second power is 64, and we flip it over, sp the answer is 1/64

Answer:

(1, −2)  (0, 1) (−1, 1)

Step-by-step explanation:

−2x+y≥−4

Substitute the points into the inequality and see if it is true

(0, −5)

-2(0) + -5 ≥−4

0-5 ≥−4

-5≥−4

False  not a solution

(1, −2)

-2(1) -2 ≥−4

-2-2 ≥−4

-4≥−4

True    it is a solution

(3, −1)

-2(3) -1 ≥−4

-6 -1 ≥−4

-7 ≥−4

False, not a solution

(0, 1)

-2(0) +1 ≥−4

0+1 ≥−4

1 ≥−4

True it is a solution

(−1, 1)

-2(-1) +1≥−4

2+1≥−4

3≥−4

True it is a solution

Answer:

(1.-2)

(0.1)

(-1,.-1)

Step-by-step explanation:

To solve this we have to plug in each point to see which one would work.

Inequality: -2x + y >= -4

First let's plugin (0,-5):

-2x + y >= -4

-2(0) + (-5) >= -4

0 - 5 >= -4

-5 >= -4 is wrong.

Now let's plugin (1,-2)

-2x + y >= -4

-2(1) + (-2) >= -4

-2 - 2 >= -4

-4 >= -4 is correct

Now let's plugin (3,-1):

-2x + y >= -4

-2(3) + (-1) >= -4

-6 - 1 >= -4

-7 >= -4 is wrong

Now let's plugin (0,1):

-2x + y >= -4

-2(0) + (1) >= -4

0 + 1 >= -4

1 >= -4 is correct

Now let's plugin (-1,1):

-2x + y >= -4

-2(-1) + (1) >= -4

2 + 1 >= -4

3 >= -4 is correct

Would appreciate if you gave me brainliest :)

Answer:

p=7Q/2

Step-by-step explanation:

Original number of students:

p students to do 1 job in 25 days.

Let r= the rate for 1 student.

pr*25=1

pr*25=1 is the work rate equation for p students.

Lesser number of students:

p-Q students came to do the job and time required was 35 days.

(P-Q)*r*35=1.

The unknowns are p, Q and r

Equate the original number of students and the lesser number of students

pr*25=(P-Q)*r*35

25rp=35rp - 35Qr

Collect like terms

25rp-35rp = -35Qr

Divide both sides by -5

-5rp+7rp=- 7rp

It can be re written as

7rp-5rp=-7Qr

2rp=7Qr

Make p the subject of the formula

p=7Qr/2r

p=7Q/2

p=7Q/2 is the original number of students

-10rp = -35Qr

The system of these two equations can be solved for p. See the THREE unknown

variables, p, r, and Q. You might assume that either r or Q would be a constant.

Answer:

The quotient is 4x-20/x+5

Step-by-step explanation:

The quotient is simply the result of the division

Through factorization, can express x^2 -25 as (x-5)(x+5)

Also x^2 + 10x + 25 as (x+5)(x+5)

and lastly 4x-44 as 4(x-11)

Now when we divide, the numerator of the second fraction will come down while the denominator goes up;

So we have ;

x^-25/x-11 * 4x-44/x^2 + 10x + 25

Now, making use of the factorizations, we have ;

(x-5)(x+5)/(x-11) * 4(x-11)/(x+5)(x+5)

Canceling out like factors, we have

= 4(x-5)/(x+5)

Answer:

(-5,-28)

Step-by-step explanation:

Use the vertex form y=a(x-h)^2

a=1

h=-5

k=-28

vertex=(h,k)

Answer:  A.  (-5, -28)

Step-by-step explanation:

f(x) = x² + 10x - 3

     a=1    b=10  

The axis of symmetry is the x-coordinate of the vertex:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(10)}{2(1)}=-5[/tex]

Input x = -5 into the original equation to find the y-coordinate of the vertex:

f(-5) = (-5)² + 10(-5) - 3

      =  25      -50    -3

      = -28

x, y coordinate of the vertex is: (-5, -28)

Answer:

28 is thee answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Solution:-

- The given question pertains to the translation of a function f ( x ) over the cartesian coordinate system.

- There are certain guidelines that must be followed when performing any translations of any function f ( x ).

Translation Guideline

  Vertical shifts

  Horizontal shifts

Where, " a " and " b " are constants for respective horizontal and vertical shifts.

- We can make a generalized form of the translated function f ( x ) to f* ( x ) as follows:

 Generalized shift: f ( x ) - > f ( x ± a ) ± b

Where,   a: Unit of horizontal shift

               b: Unit of vertical shift

- We are given a function f ( x ) defined. We are to replace the variable ( x ) with ( x + 7 ).

                          [tex]f ( x ) = x^2\\\\f^*(x) = f ( x + 7 ) = (x + 7 )^2[/tex]

- Use the above given guidelines to determine the type of shift. Take a look at the Left shift in the horizontal shift section.

- Left shift : f ( x ) -> f ( x + a ) = f ( x + 7 )

Answer: The function f ( x ) is slided a = 7 units to the left!              

Answer:

[tex]\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4[/tex]

The foci c is at +/-2√5, using c² = a² + b²:

[tex]c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2[/tex]

Substituting the value of a and b to get the equation of the hyperbola:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]

Area of a triangle is 1/2 x base x height.

The graphed triangle has height of 2 and base of 2.

Area = /2 x 2 x 2 = 2 square units.

The triangle gets enlarged by a scale factor of 2, so the new height would be 2 x 2 = 4 and the new base would be 2 x 2 = 4

Area of enlarged triangle = 1/2 x 4 x 4 = 8 square units.

The answer is C) 8

Answer:

A

Step-by-step explanation:

Answer:

264 ft³

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Height (h) = 21 ft

Radius (r) = 2 ft

Volume (V) =..?

The volume of the cylinder can be obtained as follow:

V = πr²h

V = 3.14 × 2² × 21

V = 3.14 × 4 × 21

V = 264 ft³

Therefore, the of the cylinder is 264 ft³

Step-by-step explanation:

your answer is C

HOPE IT HELPS YOU MATE

Answer:

It's 144 square units

Step-by-step explanation:

The pyramid has a square base with 8 sides and a slant height of 5

a=8

l=5

The total are of the square base pyramid is

A= [tex]a^{2}[/tex]+2al

a is side length of square and l is slant height

A= [tex](8)^{2}+2[/tex] x 8 x 5

A=64+80

A=144

Answer:

x=2.5&.5

Step-by-step explanation:

The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a

12+or-sqrt((-12^2)-4(4)(5))

12+or-sqrt(144-80)

12+or-sqrt(64)

(12+8)/8 and (12-8)/8

x=2.5 and x=.5

Answer: [tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex] or [tex]x=2.5,\:x=0.5[/tex]

Step-by-step explanation:

[tex]4x^2-12x=-5[/tex]

[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]

[tex]4x^2-12x+5=-5+5[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x^2-12x+5=0[/tex]

Solve with Quadratic Formula

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]a=4,\:b=-12,\:c=5:\quad x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]\frac{-\left(-12\right)+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]

[tex]\frac{12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=12+\sqrt{64}[/tex]

[tex]\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=\sqrt{64}[/tex]

[tex]\sqrt{64}=8[/tex]

[tex]=\frac{12+8}{8}[/tex]

[tex]=\frac{20}{8}[/tex]

[tex]=\frac{5}{2}[/tex]

[tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex]

Answer:

66.63

Step-by-step explanation:

To find the diagonal length, use Pythagorean’s theorem.

Diagonal = √45^2 + 45^2 = √2025+2025 = √4050 = 63.63.

Hope this helps

Answer:

Not a triangle

Step-by-step explanation:

Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.

Answer:

Both have the same period which is 2π

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length is 3 × width.

l = 3w

The perimeter is 24 centimeters.

P = 2l + 2w

24 = 2(3w) + 2w

24 = 6w + 2w

24 = 8w

3 = w

The width is 3 centimeters.

l = 3(3)

l = 9

The length is 9 centimeters.

Area is l × w.

A = l × w

A = 9 × 3

A = 27

The area is 27 squared centimeters.

Answer:

27

Width= x

Length= x × 3 =3x

so, 3x+3x+x+x=24

8x=24

x=24/8

x=3

so, length=3(3)=9

width=3

therefore,

Area=9×3

=27

Answer:

x = 1

Step-by-step explanation:

Given

8 - 5(x - 3) = 18 ( subtract 8 from both sides )

- 5(x - 3) = 10 ( divide both sides by - 5 )

x - 3 = - 2 ( add 3 to both sides )

x = 1

Answer:

10a²b²6ab²

Step-by-step explanation:

Distribute the 2ab the other values

Answer:

45/58.4

Step-by-step explanation:

Answer: part 1: 45/54.8.

Part 2: 55.2

Step-by-step explanation:

Edge

Answer:

(Choice C) C Infinitely many solutions.

Step-by-step explanation:

First of all, let us learn about solutions of linear equations in one variable.

The linear equations in one variable usually have one solution.

For example:

[tex]2x =x+3[/tex]

When we solve this:

[tex]2x-x=3\\\Rightarrow x=3[/tex]

One solution is [tex]x = 3[/tex]

But there can be situations when there are

1. No solutions:

For example:

[tex]x =x+9[/tex]

It means that value x is equal to value of x+9 which can never be true.

Truth is the term on Right Hand Side is always 9 greater than the value of Left Hand Side.

Such situations are called Contradictions.

Here, no solution exists.

2. Infinitely many solutions:

For example:

[tex]x+2x+8=3x+8[/tex]

The Right hand Side is just the simplification of the LHS.

And LHS is always equal to RHS no matter what is the value of variable [tex]x[/tex].

It means there are infinitely many solutions for this equation.

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

Now, let us have a look at the given equation in the question:

[tex]-4x-7+10x=-7+6x[/tex]

Taking LHS: [tex]-4x-7+10x[/tex]

Taking the terms with [tex]x[/tex] on one side:

[tex]-7+10x-4x\\\Rightarrow -7+6x[/tex]

which is equal to Right Hand Side.

Hence, as we discussed in case 2 above.

For every value of [tex]x[/tex] the equation holds true.

[tex]\therefore[/tex] There exists infinitely many solutions to the given equation.

Correct answer is:

(Choice C) C Infinitely many solutions

Answer:

C Infinitiy solutions

Step-by-step explanation: