If PT=u and QS=u–28, what is the value of u?

The positive solution of the quadratic equation [tex]\rm 0=-x^2+2x+1[/tex]  is x=2.41

It is given that the quadratic equation:

[tex]\rm 0=-x^2+2x+1[/tex]

It is required to find the solution to the above quadratic equation.

A quadratic equation is a second-degree algebraic equation represented by the:

[tex]\rm ax^2+bx+c=0[/tex]........(1)

Where a, b, and c are the constants and [tex]\rm a\neq 0[/tex]

We know that:

[tex]\rm x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have:

[tex]\rm 0=-x^2+2x+1\\\rm or \\\rm -x^2+2x+1=0[/tex] ..........(2)

After comparing (1) and (2) we get:

[tex]\rm a=-1, b=2, and \ c=1[/tex]

Put these values in the above formula we get:

[tex]\rm x=\frac{-2\pm \sqrt{2^2-(4)(-1)(1)}}{(2)(-1)}\\\rm x=\frac{-2\pm \sqrt{8}}{-2}\\\rm x=\frac{-2\pm 2\sqrt{2 }}{-2}\\\rm x={1\pm \sqrt{2}}[/tex]

[tex]\rm x=1+\sqrt{2} \ or \ x=1-\sqrt{2} \\\\\sqrt{2} = 1.41\\\rm so \ x= 1+1.41 \ or \ x= 1-1.41\\\rm x=2.41 or \ x=-0.41[/tex]

Thus, the positive solution of the quadratic equation is x=2.41

Learn more about quadratic equations here:

https://brainly.com/question/2263981

Answer:

x= 2.41

Step-by-step explanation:

1)

[tex]m = \frac{y - y}{x - x} = \frac{55 - 59}{10 - 0} = \frac{ - 4}{10} = - \frac{2}{5} [/tex]

[tex]y = - \frac{2}{5} x + b[/tex]

Since the line passes through the point (0,59), the coordinates of this point satisfies the equation of y;

[tex]59 = - \frac{2}{5} (0) + b[/tex]

[tex]b = 59[/tex]

Final answer:

[tex]y = - \frac{2}{5} x + 59[/tex]

Answer:

-12 < x  

or:

x > -12

Step-by-step explanation:

[tex]5 > -x-7[/tex]

[tex]5+7 > -x[/tex]

[tex]12 > -x[/tex]

[tex]12(-1) > -x(-1)[/tex]

[tex]-12 < x[/tex]

Hope this helps

Answer: 12.5 square centimeters

Step-by-step explanation:

Answer:

The value of x is equal to 1, written as x = 1.

General Formulas and Concepts:
Algebra I

Equality Properties

Terms/Coefficients

Functions

Step-by-step explanation:

Step 1: Define

g(x) = 5x + 4

g(x) = 9

Step 2: Solve for x

∴ when the function g(x) equals 9, the value of x that makes the function true would be x = 1.

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Topic: Algebra I

Answer:

f/6 - 20 = 34.75

f = -88.5

Step-by-step explanation:

-88.5/6 = -14.75

-14.75 - 20 = 34.75

Answer:

2×2×13 = 52

or 2² × 13 = 52

it depends on how you want to present your answer

Answer:

around 433.1 cm

find the first shape's volume.

L x W x H method.

[tex]4 * 10 * 8 = 320cm[/tex]

Length is eight, height is 4, and width is 10.

Now, the 2nd shape.

The formula of finding a sphere with a radius of 3 is V = 4/3[tex]pi^3[/tex]

In that case, the answer should be an estimated 113.1

Add the two cm's together.

[tex]320 + 113.1 = 433.1[/tex]

Please note that this is rounded to tenths place and estimated.

Please mark brainliest. Thanks! :)

First of all we will divide the figure in two shapes. One is hemisphere and other is a cuboid.

Volume of hemisphere:

[tex] \boxed{ \tt \:v = \frac{2}{3} \pi {r}^{3} }[/tex]

Volume of cuboid:

[tex] \boxed{ \tt \: v = length \times breadth \times height}[/tex]

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex] \sf \dashrightarrow \: v = \frac{2}{3} \times \frac{22}{7} \times {3}^{3} [/tex]

[tex] \sf \dashrightarrow \: v = \frac{2}{ \cancel3} \times \frac{22}{7} \times \cancel{27}[/tex]

[tex] \sf \dashrightarrow \: v = 2 \times \frac{22}{7} \times 9[/tex]

[tex] \sf \dashrightarrow \: v = \frac{396}{7} [/tex]

[tex] \sf \dashrightarrow \: v = 56.6 \: {cm}^{3} [/tex]

[tex] \bf \multimap \: v = 8 \times 10 \times 4[/tex]

[tex] \bf \multimap \: v = 80 \times 4[/tex]

[tex] \bf \multimap \: v = 320 \: {cm}^{3} [/tex]

[tex] \rm \leadsto \: total \: volume = 56.6 + 320 \: {cm}^{3} [/tex]

[tex] \rm \leadsto \: total \: volume = 376.6\: {cm}^{3} [/tex]

If we round to the nearest tenth the total volume is ᭄

[tex] \rm \twoheadrightarrow volume = 380 \: {cm}^{3} [/tex]

Answer:

4300 [tex]\frac{67}{1000}[/tex]

Step-by-step explanation:

evaluate each part

4 × 1000 = 4000

3 × 100 = 300

6 ×[tex]\frac{1}{100}[/tex] = [tex]\frac{6}{100}[/tex] × [tex]\frac{10}{10}[/tex] = [tex]\frac{60}{1000}[/tex]

7 × [tex]\frac{1}{1000}[/tex] = [tex]\frac{7}{1000}[/tex]

Thus

4000 + 300 + [tex]\frac{60}{1000}[/tex] + [tex]\frac{7}{1000}[/tex]

= 4300 [tex]\frac{67}{1000}[/tex]

Answer:

X= -3 or X=-9

Step-by-step explanation:

Answer: x = -3, x = -9

Step-by-step explanation: |x + 6| + 10 = 13

Firstly, subtract 10 from both sides:

|x + 6| = 3

Since it is an absolute value, separate it into two equations with either outcome:

x + 6 = 3

x + 6 = -3

Solve for x now.

x + 6 = 3

Subtract 6 from both sides:

x = -3

x + 6 = -3

Subtract 6 from both sides:

x = -9

Voila! Hope this helps.

Answer:

[tex]\sf 35 \%[/tex]

explanation:

[tex]\hookrightarrow \sf \dfrac{orange \ juice \ intake}{recommended \ mg} * 100[/tex]

[tex]\hookrightarrow \sf \dfrac{7*100}{2000} *100[/tex]

[tex]\hookrightarrow \sf 35 \%[/tex]

Answer:

Step-by-step explanation:

100x7=700

So you ate 700mg of Vitamin C by eating oranges 7 times in that day.

Now, lets figure out the percent part

700 n/100x2000

=35%

We didn't even have to round.

So hence, your answer is B.35%

Thanks!

Mark me brainliest!

Answer:

-2

Step-by-step explanation:

-8 + 2 = -6; -6=3y; then -6 divided by 3 = -2

Answer:

See below.

Step-by-step explanation:

a) Complementary angles (= 90°)

b) ∠FMG, ∠GMC, and ∠DMC

Answer:

The answer is below

Step-by-step explanation:

Given the cost as C(x) = x² + 4x - 40

a) Since the bracelets sell for $8 each, the revenue from x bracelets is given as:

Revenue = price for each bracelet × number of bracelet

Revenue = 8 × x = 8x

b) Profit (P) = Revenue - Cost

P(x) = 8x - [x² + 4x - 40]

P(x) = 8x - x² - 4x + 40

P(x) = -x² + 4x + 40

c) To maximize profit, the derivative of profit is equal to 0

Hence P'(x) = 0

-2x + 4 =0

2x = 4

x = 2

To maximize profit, the company should produce 2 bracelets

d) The maximum profit is:

P(2) = -(2²) + 4(2) + 40 = -4 + 8 + 40

P(2) = $44

The maximum profit is $44

Hey there!

1/5 + 3/10
= 2/10 + 3/10

= 2 + 3/10 - 0

= 5/10

= 5 ÷ 5 / 10 ÷ 5

= 1 / 2

Therefore, your answer is: 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

YES

Step-by-step explanation:

To solve this inequality, you need to multiply both sides by -5.

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.

Answer: YES

We are given that :

Using Formulas:

Area of rectangle:

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak {length\times breadth }}}[/tex]

Area of semicircle:

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak{ \dfrac{\pi r^2 }{2}}}}[/tex]

Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;

[tex] \quad\dashrightarrow\quad \sf {Area_{\tiny { total}} = Area_{\tiny {rectangle}}+ Area_{\tiny {semicircle}}}[/tex]

[tex] \quad\dashrightarrow\quad \sf {A = ( l \times b ) + \dfrac{\pi r^2 }{2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {41.4 = ( l \times 4 ) +\dfrac{3.14\times 2^2}{2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4= ( l \times 4 )+ \dfrac{ 3.14\times 4}{2}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4=( l \times 4 )+ \dfrac{12.56}{2}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4= (l \times 4 )+ 6.28}[/tex]

[tex] \quad\dashrightarrow\quad \sf {l \times 4 = 41.4-6.28 }[/tex]

[tex] \quad\dashrightarrow\quad \sf { l\times 4 = 35.12}[/tex]

[tex] \quad\dashrightarrow\quad \sf { l =\dfrac{35.12}{4}}[/tex]

[tex] \quad\dashrightarrow\quad \underline{\underline{\pmb{\sf {l = 8.78\:cm}}} }[/tex]

The length of the longer side of the rectangle will be 8.78 cm.

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

On one of a rectangle's shorter sides, a semicircle is drawn. The rectangle's shorter side is 4 cm long. The figure has a surface area of 41.4 square centimeters.

Then the length of the rectangle is calculated as,

A = πr² / 2 + l × b

41.4 = (3.14 / 2) × (4/2)² + 4l

41.4 = 6.28 + 4

l = 8.78 cm

The length of the longer side of the rectangle will be 8.78 cm.

More about the area link is given below.

https://brainly.com/question/27683633

#SPJ3

Answer:

15

Step-by-step explanation:

The cards have 5 possible outcomes and the spinner has 3 possible outcomes. To find the sample size, you need to calculate the number of possibilities when drawing 1 card and landing on 1 side of the spinner. You can do this by multiplying the possible outcomes together.

5×3 = 15

Therefore, the sample size is 15.

Answer:

Option 1: 15

Step-by-step explanation:

Ricky is playing a game using 5 cards and a spinner

Card 1 , Card 2 , Card 3 , Card 4 , Card 5

and

㉦ Green, Red, Blue

Ricky picks a card and spins the spinner

The sample size outcome is:

{(1, G) (1, R) (1, B) (2, G) (2, R) (2, B) (3, G) (3, R) (3, B) (4, G) (4, R) (4, B) (5, G) (5, R) (5, B)}

Sample size is 15

d = rt

d/r  rt/r

d/r = t

Answer:

-10xy

Step-by-step explanation:

Answer:

-10xy

Step-by-step explanation:

distributive property

5*-2=-10

-10xy

Answer:

Neither are monomials.

Step-by-step explanation:

Take a look at the root word of monomials.

Answer:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Step-by-step explanation:

..

Answer: 30 days.

Step-by-step explanation: Figure out the least common multiple for each number.

Answer:

you forgot to distribute 2 into the -3

I'm going to assume you ment 8

Step-by-step explanation:

2(x-3)=5

2x-6=5

+6 to both sides

2x=11

÷2 both sides

x = 5.5

Answer:

5x + 6y

Hope it helps!

Answer:

arc QS = 95°

Step-by-step explanation:

the inscribed angle QSR is half the measure of its intercepted arc RQ , then

arc RQ = 2 × 95° = 190°

the sum of the arcs in a circle = 360° , then

arc QS = 360° - arc SR - arc RQ = 360° - 75° - 190° = 95°

Answer:

30

Step-by-step explanation:

5z + 20 + 10 - 5z

= 5z - 5z+ 20 + 10

= 30

While guessing and checking is one way to do this problem, I will show you how to do it algebraically.

Let one side be A

Let the other side be B

2(A+B)=16

A*B=15

First equation because the perimeter is 16 and the second because the area is 15. Now solve the system of equations

A+B=8

A=8-B

Substitute into equation two

B(8-B)=15

-B^2+8b-15=0

B^2-8b+15=0

(B+3)(B+5)=0

B=3,5

A=5,3 respectively

From this we can see that one side is 5 meters long while the other side is three meters long.

Step-by-step explanation

Since we're looking at a rectangle, let's consider its perimeter and area formulas.

Perimeter: 2x + 2y (A rectangle has four sides, with two equal sides, so this is x + x + y + y simplified)

Area: (x)(y) (length x breadth so, x times y)

So we have two equations: 2x + 2y = 16 and x*y = 15. Solve simultaneously. Refer to the attached image.

Answer:

Step-by-step explanation:

Converse of alternate interior angles theorem:

This theorem states that if two lines are intersected by a transversal and the alternate interior angles are congruent, lines will be parallel.

Therefore, p║n.

Perpendicular transversal theorem:

By this theorem,

In a plane, if a line is perpendicular to one of two parallel lines, then it will be perpendicular to the other line.

Therefore, l ⊥ p.

Options selected in the blank spaces are correct.