10y^2+10y+3=0 use quadratic formula to solve each equation ​

Final answer:

Option B: x + (y - z) is equivalent to the given expression (x + y) - z, applying the principles of associativity of addition and subtraction.

Explanation:

The question asks which of the given expressions are equivalent to (x + y) - z. To find the equivalent expressions, we need to apply the principles of commutativity and associativity of addition and subtraction.

Option A: z + (x + y) is not equivalent because the order of operations affects the result due to the subtraction of z. By combining z at the beginning, it implies adding before subtracting z, which alters the outcome unless z is explicitly negated.

Option B: x + (y - z) is equivalent. You can alter the grouping of addition due to associativity (x + y) - z = x + (y - z). Subtracting z directly from y before adding to x does not change the result.

Option C: None of the above is incorrect because Option B is indeed equivalent to the original expression.

Therefore, the expression that is equivalent to (x + y) - z is Option B: x + (y - z).

Answer:

y-2=x-5

Step-by-step explanation:

First, I don't remember about how to solve point slope form, just go and search about how to solve point slope form on Google.

Simplifying

0.5p + -3.45 = -1.2

Reorder the terms:

-3.45 + 0.5p = -1.2

Solving

-3.45 + 0.5p = -1.2

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '3.45' to each side of the equation.

-3.45 + 3.45 + 0.5p = -1.2 + 3.45

Combine like terms: -3.45 + 3.45 = 0.00

0.00 + 0.5p = -1.2 + 3.45

0.5p = -1.2 + 3.45

Combine like terms: -1.2 + 3.45 = 2.25

0.5p = 2.25

Divide each side by '0.5'.

p = 4.5

Simplifying

p = 4.5

The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 0.5p-3.45=-1.2

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

0.5p-3.45=-1.2

0.5p= -1.2+3.45

0.5p= 2.25

p= 2.25/0.5

p= 4.5

Therefore, the value of p is 4.5.

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Answer:

I think the D equals one (1) based on the info i was given

Step-by-step explanation:

Answer:

d = 6 units

Step-by-step explanation:

Circumference of the circle is given by:

[tex]C = \pi d[/tex]

where, d is the diameter of the circle.

As per the statement:

Given a circle 1 with measures of (C, d, and r) and a circle 2 with measures of (C', d', and r').

Circumference of a circle(C) 1 with diameter(d) is given by:

[tex]C = \pi d[/tex]               .....[1]

Also, the circumference of a circle (C') 2 with diameter(d') is given as:

[tex]C' = \pi d'[/tex]

Divide equation [1] and [2] we have;

[tex]\frac{C}{C'} = \frac{\pi d}{\pi d'}[/tex]

⇒[tex]\frac{C}{C'} = \frac{d}{d'}[/tex]

Substitute the given values [tex]\frac{C}{C'}=12[/tex] and d' = 0.50 then;

[tex]12 = \frac{d}{0.50}[/tex]

Multiply both sides by 0.50 we have;

6 = d

or

d = 6 units

Therefore, the value of d is, 6 units

Answer: [tex](-\frac{5}{7})^{17}[/tex]

Step-by-step explanation:

The expression can be simplified by applying the a properties of exponents, specifically the Product of powers, which states that:

[tex](b^a)(b^c)=b^{(a+c)[/tex]

Where b is the base and a and c are exponents.

 Then simplify it by rewriting the base ([tex]-\frac{5}{7}[/tex]) and adding the exponents of the expression (8 and 9).

You will get the expression simplified and written as a power:

[tex](-\frac{5}{7})^8(-\frac{5}{7})^9=(-\frac{5}{7})^{(8+9)}=(-\frac{5}{7})^{17}[/tex]

Final answer:

To simplify the expression [tex](- 5/7)^8\times (- 5/7)^9[/tex], add the exponents of the same base to get [tex](-5/7)^{17}[/tex], which is the simplified expression written as a power.

Explanation:

To simplify the expression and write the answer as a power when you have [tex](- 5/7)^8\times (- 5/7)^9[/tex], you can use the property of exponents that states when you multiply expressions with the same base, you add their exponents.

This means the simplified expression will be [tex](- 5/7)^8[/tex]+9, which equals [tex](-5/7)^{17}[/tex]. The negative base raised to an odd power remains negative, resulting in a negative final answer.

Answer:

(f º f)(3) = 30, when f(x) = x² - x

Step-by-step explanation:

This is a great example of composite functions and how to multiply one function by another.  (f º f) really means f(f(x)), or replacing every x in the original function f(x) with the function f(x).

Step 1: State the original function.

[tex]f(x) = x^{2} -x[/tex]

Step 2: Insert the function f(x) wherever there is an x.

[tex]f(f(x))=(x^{2} -x)^{2} -(x^2-x)[/tex]

Step 3: Expand anything that has an exponent. Remember: [tex](x+y)^2 = (x+y)(x+y)[/tex]

[tex]f(f(x))=(x^{2} -x)(x^{2} -x) -(x^2-x)[/tex]

Step 4: Foil the parts of the equations in brackets by multiplying the first terms, outside terms, inside terms and last terms in each bracket.

[tex]f(f(x))=(x^{4}-x^3-x^3+x^{2}) -(x^2-x)[/tex]

Step 5: Now you can remove the brackets (don'f forget to switch the symbols for the second brackets because you are subtracting) and sum the like terms.

[tex]f(f(x))=x^{4}-x^3-x^3+x^{2} -x^2+x[/tex]

[tex]f(f(x))=x^{4}-2x^3+x[/tex]

Step 6: Finally, substitute the given x value, which is 3, into the new equation.

[tex]f(f(x))=(3)^{4}-2(3)^3+(3)[/tex]

[tex]f(f(x))=81-54+3[/tex]

[tex]f(f(x))=30[/tex]

Therefore the answer is (f º f)(3) = 30.

Answer:

30

Step-by-step explanation:

Method 1:

ƒ(x) = x² - x

(f∘f)(x) = f(f(x)) = f(x²-x) = (x² - x)² - (x² - x) = x⁴ - 2x³ + x² - x² + x =  x⁴ - 2x³ + x

(f∘f)(3) = 3⁴ - 2(3)³ + 3 = 81 - 54 + 3 = 30

Method 2:

f(3) = 3² - 3 = 9 - 3 = 6

(f∘f)(3) = f(f(3)) = f(6) = 6² - 6 = 36 - 6 = 30

Answer:

567.63

Step-by-step explanation:

To find the discount, take the original price times the discount percent

discount = 765*30%

               = 765 *.3

               =229.5

The new price is  the original price minus the discount

new price =765-229.5

                 =535.50

Now we need to find the tax.  Tax is the new price times the tax rate

tax =535.5 * 6%

      535.5*.06

       32.13

To find the final price. we add the tax to the new price

final price = new price + tax

                  =535.5+32.13

                  567.63

Answer:

16 bags

Step-by-step explanation:

To find this, we divide 2 over 1/8, to see how many units of 1/8 fits into that of 2.

[tex]\frac{2}{\frac{1}{8} }[/tex] can be rewritten as 2*8. 2*8 = 16 bags.

Answer:

16 bags

Step-by-step explanation:

We are given that Lin is making small bags of trail mix for campers and has 2 pounds of raisins.

If she puts 1/8 pound in each bag, we need to find out how many bags can she fill before she runs out of raisins.

To find this, we just need to divide the pounds of raisins by the amount of raisins she is putting in each bag.

Number of bags Lin can fill = [tex]\frac{2}{\frac{1}{8} }[/tex] = 16

Answer:

The answer is A (APEX)

Answer:

Step-by-step explanation:

Given is table of x,y as follows:

x   y

1    4

2    8

3   27

4  85

5  250

6  600

The nearest seems to be from

y = 1.24(2.84)^x

Answer:

Step-by-step explanation:

8x - 2y + x + x        combine like terms

= (8x + x + x) - 2y

= 10x - 2y

The circle area can be defined as x2 + y2 < 3.46^2.

For point M, x2 + y2 = 13.

Since 3.46^2 is about 12, point M is outside the circle!

Answer:

outside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius = 3.46410161514, hence

x² + y² = 3.46410161514²

x² + y² = 12 ← equation of circle

To determine where a point (x, y) lies

• If x² + y² < r² then point is inside the circle

• If x² + y² = r² then point lies on the circle

• If x² + y² > r² then point lies outside the circle

For (- 3, 2)

(- 3)² + 2² = 9 + 4 = 13 > 12

Hence point (- 3, 2) lies outside the circle

Answer:

Top one

Step-by-step explanation:

turn b² into a fraction of h, so b2h/h

For this case we have the following equation to find [tex]b_ {1}[/tex]

[tex]b_ {1} = \frac {2A} {h} -b_ {2}\\\\[/tex]

If we want to find an equivalent equation, we do the following:

[tex]\frac{2A}{h}-b_{2}=\frac{2A*1-b_{2}*h}{h}=\frac{2A-b_{2}h}{h}\\\\[/tex]

So, we have to:

[tex]b_ {1} = \frac {2A} {h} -b_ {2} = \frac {2A-b_ {2} h} {h}\\[/tex]

Answer:

Option A

Answer:

[tex]a\geq -5[/tex]

Answer:

$12

Step-by-step explanation:

Let p be the store's cost (cost to buy the product wholesale).

Then the selling price is p + markup, or

                                         p + 0.80p = 1.80 p

and this comes to $21.60.

Dividing $21.60 by 1.80 results in p = $12.

The cost to the store is $12.

Answer:

Step-by-step explanation:

20 = -d + 16          subtract 16 from both sides

20 - 16 = -d + 16 - 16

4 = -d               change the signs

-4 = d ⇒ d = -4

Answer:

The correct answer option is: Yes, because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow .

Step-by-step explanation:

We are given that Elias writes the numbers 1 through 20 on separate slips of paper.

Given that there are 16 white slips and four yellow slips and  eight odd numbers on white slips, and the rest of the odd numbers are on yellow slips, we can conclude that the events are odd and yellow independent because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow .

Answer:

c

Step-by-step explanation:

Circumference is 2 times the radius times PI.

2 x 3 = 6

6 x 3.14 = 18.84  

The circumference is 18.84 inches.

Answer:

centre = (- 3, - 8), radius = [tex]\sqrt{6}[/tex]

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 3)² + (y + 8)² = 6 ← is in standard form

with centre = (- 3, - 8) and r = [tex]\sqrt{6}[/tex]

I’m assuming it’s 15

Answer: 30

Step-by-step explanation: First of all, you need to know that the angle at hand is a right angle which measures up to 90 degrees. Knowing this, subtracting 90-30 will give you the result of 60 which is the measure of the unknown angle. Now, you know that 60=2x, so divide both sides by 2 and you get 30=x.

Also, this isn't part of the answer, but can you tell me how you added the pic?

Answer:

The value of x is 13

Step-by-step explanation:

* Lets study the to circles

- The are congruent

- The length of chord TS equal to the length of chord UV

- The measure of the minor arc TS equal to the measure

 of minor arc UV

- The measure of the major arc TS equal to the measure

 of major arc UV

* We now that the measure of any circle = 360°

∴ The sum of the measure of the minor arc and the measure

  of the major arc equal to 360°

* In circle Q:

∵ The measure of the major arc UV is 22x - 13°

∵ The measure of the minor arc UV is 10x - 43° ⇒ circle R ≅ circle Q

∵ The sum of the measure of the two arcs = 360°

∴ 22x - 13 + 10x - 43 = 360 ⇒ add the like terms

∴ 32x - 56 = 360 ⇒ add 56 to both sides

∴ 32x = 416 ⇒ divide both sides by 32

∴ x = 13

* The value of x is 13

Answer:

quotient

Step-by-step explanation:

A multiple of a number refers to the product of that number and any whole number. When a number is multiplied by itself, it's referred to as exponentiation where the number being multiplied is the base, and the times it is multiplied is the exponent.

The student's question seems to be about the concept of multiplication in Math. A multiple of a number refers to the result of multiplying a number by any whole number. This is basically the process of addition repeated. For instance, the multiples of 3 include 3 (3x1), 6 (3x2), 9 (3x3), etc.

When a number is multiplied by itself a certain number of times, this takes on a different meaning. This operation is called exponentiation, where the number that is being multiplied is the base, and the number of times it's being multiplied is the exponent. For instance, 32 means 3 is being multiplied by itself 2 times (3 x 3), which equals 9. If we say 53, that means 5 is being multiplied by itself 3 times (5 x 5 x 5), which equals 125.

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The MAD for this set of number is 0.36

Answer:

See explanation

Step-by-step explanation:

If PK and PF are tangent to the circle, then the radii OK and OF are perpendicular to the lines PK and PF respectively.

Consider quadrilateral PFOK. The sum of the measures of all interior angles in quadrilateral PFOK is equal to 360°. Since OK and OF are perpendicular to the lines PK and PF, you have that

∠FOK+90°+∠KPF+90°=360°,

∠FOK=360°-90°-90°-∠KPF=180°-∠KPF.

Angles FOK and KOE are supplementary angles, then

∠KOE=180°-∠FOK=180°-(180°-∠KPF)=∠KPF.

Since angle KOE is central angle, the arc EK has the same measure as angle KOE and as angle KPF.

Given [tex]\(PK\) and \(PF\)[/tex] tangents to circle [tex]\(O\),[/tex] angles [tex]\( \angle P \) and \( \angle EK \)[/tex] are equal by the properties of tangents.

To prove that [tex]\( m\angle P = m\angle EK \)[/tex] given the diagram, we can use properties of tangents and circles. Here is a step-by-step proof:

1. Identify the given information:

  - [tex]\( PK \) and \( PF \)[/tex] are tangents to circle [tex]\( k(O) \) at points \( K \) and \( F \),[/tex] respectively.

  - [tex]\( O \)[/tex] is the center of the circle.

  - [tex]\( PK \) and \( PF \)[/tex] are tangent to the circle, meaning they touch the circle at exactly one point.

2. Use properties of tangents:

  - A tangent to a circle is perpendicular to the radius at the point of tangency.

  - Thus, [tex]\( OK \perp PK \) and \( OF \perp PF \).[/tex]

3. Mark the right angles:

[tex]- \( \angle OKP = 90^\circ \)[/tex]

[tex]- \( \angle OFP = 90^\circ \)[/tex]

4. Connect the points to form a triangle:

  - Draw the line segment [tex]\( OP \).[/tex]

5. Use the exterior angle theorem:

  - In [tex]\(\triangle OKP\),[/tex] [tex]\( \angle OPK \)[/tex] is an exterior angle for [tex]\(\angle OKP\) and \(\angle PKO\).[/tex]

  - Since [tex]\( \angle OKP = 90^\circ \)[/tex] and [tex]\(\angle PKO\)[/tex] is another angle in the triangle, we have:

[tex]\[ \angle OPK = 180^\circ - (\angle OKP + \angle PKO) = 180^\circ - (90^\circ + \angle PKO) = 90^\circ - \angle PKO. \][/tex]

6. Similarly, in [tex]\(\triangle OFP\):[/tex]

  -[tex]\( \angle OFP = 90^\circ \) and \(\angle PFO\)[/tex] is another angle in the triangle.

  - Using the same logic as before:

[tex]\[ \angle OEP = 180^\circ - (\angle OFP + \angle PFO) = 180^\circ - (90^\circ + \angle PFO) = 90^\circ - \angle PFO. \][/tex]

7. Note that [tex]\( \angle OKP = \angle P \)[/tex] and [tex]\( \angle OFP = \angle EK \):[/tex]

  - By the property of the tangents from the same external point, [tex]\( PK = PF \).[/tex]

  - [tex]\( \angle PKO \) and \( \angle PFO \)[/tex] are complementary to [tex]\(\angle P\)[/tex] and [tex]\(\angle EK\)[/tex] respectively.

Therefore, it follows that:

[tex]\[ m\angle P = m\angle EK \][/tex]

Thus, the proof is complete.

I think line k I'm not sure

Answer:

Point X is the correct answer.

Step-by-step explanation:

The point X is on the line M in plane A

Answer:

L: 8in W: 2in H: 22in

Step-by-step explanation:

Answer:

     $34,505

s = --------------- = $33,500

         1.03

Step-by-step explanation:

Last year's salary was 1.00 s.

A 3% pay raise would thus amount to 0.03s.

This would equal this year's salary:  $34,505.

Thus, 1.03s = $34,505; find s, which was last year's salary.

Dividing both sides by 1.03, we get:

     $34,505

s = --------------- = $33,500

         1.03

The answer is −2.4x2−1.5x−11.4

Let's simplify step-by-step.

−4.1x2+0.9x−9.8+1.7x2−2.4x−1.6

=−4.1x2+0.9x+−9.8+1.7x2+−2.4x+−1.6

Combine Like Terms:

=−4.1x2+0.9x+−9.8+1.7x2+−2.4x+−1.6

=(−4.1x2+1.7x2)+(0.9x+−2.4x)+(−9.8+−1.6)

=−2.4x2+−1.5x+−11.4

Answer:

60 is c not d

Step-by-step explanation:

Answer:

c. m∠ABC = 60°

Step-by-step explanation:

E2020

Answer:

1

Step-by-step explanation:

it would be one because then it wouldn't have been dilated cause dilation is a non-rigid transformation and would no have kept the congruence of the original shape.

Answer:

28

hope this helps

Answer:

34 is the median of the following data set.

Step-by-step explanation:

We have given a data set of values.

28,45,12,34,36,19,20

We have to find median of the given data set.

Median is defined as the middle value of the ordered data set.

Putting given data set in order , we have

12,19,20,28,34,36,45

Hence, the middle value is 28.

So, median is 34  for given data set.