The graph below shows a system of equations: Draw a line labeled y equals minus x plus 5 by joining the ordered pairs 0, 5 and 5, 0. Draw a line labeled y equals x minus 1 The x-coordinate of the solution to the system of equations is ___ . (5 points)

Answer:

-1/2

Step-by-step explanation:

The equation given is

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

Write it in form of y=mx+c where m is the gradient and c is the y-intercept

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

y-intercept is -1/2

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem we have

[tex]m=-\frac{1}{3}[/tex]

[tex]b=-3[/tex]

substitute

[tex]y=-\frac{1}{3}x-3[/tex]

To graph the line find out the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y=-\frac{1}{3}(0)-3=-3[/tex]

The y-intercept is the point (0,-3) -----> is a given value

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]0=-\frac{1}{3}x-3[/tex]

[tex]x=-9[/tex]

The x-intercept is the point (-9,0)

Plot the intercepts and join the points to graph the line

see the attached figure

To graph the line with a slope of -1/3 and a y-intercept of -3, plot the y-intercept at (0, -3) and use the slope to find additional points. Connect the points to graph the line.

To graph the line with a slope of -1/3 and a y-intercept of -3, we can start by plotting the y-intercept at the point (0, -3). Then, using the slope, we can find additional points on the line. Given that the slope is -1/3, we can move down 1 unit and to the right 3 units from the y-intercept to find the next point. We can continue this process to find more points and then connect them to graph the line.

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[tex]4(4a+6b) =16a+24b[/tex]

Answer:

B. repeating

Step-by-step explanation:

An irrational number written in  decimal form will be nonterminating  and non-repeating  decimals.

For example we have √2 = 1.4142

This rational number is non-terminating and non-repeating.

Answer:

repeating

Step-by-step explanation:

Answer:

y = 2½x - 14

Step-by-step explanation:

You simply do this:

-29 = 5⁄2[-6] + b; -14 = b

-15

Now remember, parallel rate of changes [slopes] have SIMILAR slopes, so they remain the same.

**2½ = 5⁄2 [Do not worry]

I am joyous to assist you anytime.

Answer:

7/5

Step-by-step explanation:

Slope intercept form is y=mx+b. It is called that because it tells us the slope,m, and the y-intercept, b.

So we can solve your given equation to find m the slope.

7x-5y=10

Subtract 7x on both sides:

-5y=-7x+10

Divide both sides by -5

y=(-7/-5)x+(10/-5)

Simplify:

y=(7/5)x+-2

m=7/5 so 7/5 is the slope.

Hello! What is this for?

Also, The answer is: The lead pattern would be in the shape of a circle.

Answer: The Circle!

Step-by-step explanation:

just took the test!

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

[tex]\frac{7\pi }{6}[/tex] is in the third quadrant

To find the reference angle subtract π from it, that is

reference angle = [tex]\frac{7\pi }{6}[/tex] - π = [tex]\frac{\pi }{6}[/tex]

Answer:

[tex]\large\boxed{x^\frac{5}{3}y^\frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\ \text{and}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\\\\sqrt[3]{x^5y}=\sqrt[3]{x^5}\cdot\sqrt[3]{y^1}=x^\frac{5}{3}y^\frac{1}{3}[/tex]

Answer:

B

Step-by-step explanation:

edge 2021

This was too long for me to write on the computer.

So I wrote it and took a picture.

If you have any questions, please don't hesitate to ask in the comments.

AB= 20 and AB is the full line.

We will have to divide the length of the segment by 2 to find AC.

20/2= 10

AC is 10 units. Hope this helps!

Answer: the answer is: AC= 10

Step-by-step explanation:

you can imagine a line that represents AB with 20cm of large and the midline is located in the middle of this line; this means that AC is the half of AB

So in number=

[tex]AC= AB/2[/tex]

replacin [tex]AB[/tex]

[tex]AC= 20/2[/tex]

[tex]AC=10[/tex]

Answer: The answer is A

Step-by-step explanation:

Its the only one that has the least amount of options and the highest probability chance

Answer:

The equation would be x²/a² - y²/b² =1 , x²/9 - y²/40 = 1 ....

Step-by-step explanation:

The standard equation of hyperbola with a horizontal transverse axis is:

(x-h)²/a² - (y-k)² /b²  = 1

Use Pythagorean theorem to find the value of b.

c² = a²+b²

c= 7

a = 3

Put the value in the equation:

(7)² = (3)² +b²

49= 9+b²

49-9 = b²

40 = b²

Square root both sides:

√40 = √b²

√40 = b

Assume that the center of hyperbola is(0,0)

Thus

(x-0)²/a²  - (y-0)²/b² = 1

x²/a² - y²/b² =1

x²/(3)² - y²/(√40)² = 1

x²/9 - y²/40 = 1

Therefore the equation would be x²/a² - y²/b² =1 , x²/9 - y²/40 = 1 ....

Answer:

[tex]\dfrac{x^{2}}{9} - \dfrac{y^{2}}{40}} = 1[/tex]

Step-by-step explanation:

The standard form of the equation of a hyperbola with center (0,0) and horizontal transverse axis is

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

and the distance c between the foci and the y-axis is given by

c² = a² + b²

1. Calculate b

7² = 3² + b²

49 = 9 + b²

40 = b²

b = √40

2. Write the equation

[tex]\dfrac{x^{2}}{3^{2}} - \dfrac{y^{2}}{(\sqrt{40})^{2}} = 1\\\\\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{40}}} = \mathbf{1}[/tex]

The figure shows your hyperbola with a horizontal transverse axis and c = 3.

[tex]8x=2^3\cdot x\\40y=2^3\cdot5\cdot y\\\\\text{gcf}(8x,40y)=2^3=8[/tex]

Answer:

-7 +c

Step-by-step explanation:

(7-c)(-1)

Distribute the -1

-1*7 -1*(-c)

-7 +c

Answer:

8

15

Step-by-step explanation:

To find the GCF of numbers, first find the prime factorizations of the numbers. The GCF is the product of common factors with lowest exponent.

GCF (16, 24)

16 = 2^4

24 = 2^3 * 3

GCF = 2^3 = 8

GCF (15, 45, 60)

15 = 3 * 5

45 = 3^3 * 5

60 = 2^2 * 3 * 5

GCF = 3 * 5 = 15

Answer:

A=8, B= 15

Step-by-step explanation:

Answer:

I just got done doing this. Full answers to all 4 problems are down below. All correct answers are bolded.  

Step-by-step explanation:

First problem: x2 + -8 x = 9

Add 16 to each side x2 – 8x = 9 to complete the square.

Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation. Answer: (x – 4)² = 25

Choose the solutions to the quadratic equation x2 – 8x – 9 = 0. Answer: -1, 9  

The equation x² - 8x - 9 = 0 can be written as x² +(-8x) = 9 which is of the form  x² + bx = c  where,

b = -8

c = 9

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

The given equation is

x² - 8x - 9 = 0.

⇒ x² - 8x = 9

⇒ x² +(-8x) = 9

So the given equation is written of the form x² + bx = c, where,

b = -8

c = 9

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Answer:

Option C is correct.

Step-by-step explanation:

We are given

1452 divided by 44 = (1452 divided by 4) divided by 11

We know that 44 = 4*11

So, 4 and 11 are factors of 44.

This division problem uses the method of Factors.

Option C is correct.

Answer:

The equation is:

[tex]y=2500t+75000[/tex] where t is the number of years satisfying the inequality [tex]0\let\le5[/tex] and y is the population at that time.

Step-by-step explanation:

So it gives us the initial amount 75000; this is what happens at time 0.

So we have the point (0,75000) is on the function's graph.

(0,75000)

(1,77500)  -> It goes 2500 per year. So year 1 the population is 75000+2500.

So we have the y-intercept of the line which is (0,75000).

We just need the slope.

Our goal is to put into slope-intercept form: y=mt+b form where m is the slope and b is the y-intercept.

To find the slope, you line up the points vertically and subtract then put 2nd difference over 1st difference.

(  1   ,   77500 )

-( 0  ,    75000)

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

 1           2500

So the slope is 2500/1=2500 which we should have known earlier since the y's are increasing by 2500 while the x's are increasing by 1.

So while t is between 0 and 5 inclusive we have the following equation:

y=2500t+75000

1. 12 mph, 24 miles

2. m=4, y=22

3.15/1, $1500

4. x=30 y=60, k cheaper, j cheaper

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&2,625\\ P=\textit{original amount deposited}\dotfill & \$25,000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years \end{cases} \\\\\\ 2625=(25000)(0.035)t\implies \cfrac{2625}{(25000)(0.035)}=t\implies 3=t[/tex]

Answer:

The  number of years = 3 years

Step-by-step explanation:

Points to remember

Simple interest

I = PNR/100

Where P - Principle amount

N - Number of years

R - Rate of interest

To find the number of years

Here P = 25,000

R = 3.5% and I = 2625

I = PNR/100

N = (I * 100)/PR

 = (2625 * 100)/(25000 * 3.5)

 = 3 years

Therefore number of years = 3 years

Answer:

352.8 feet

Step-by-step explanation:

The given triangle is drawn in the image attached with. Note that the image is not drawn to scale.

We can find the length of AB using the law of sines. According to which:

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Since sum of angles in a triangle is 180, we can write:

A + B + C = 180

A + 102.9 + 18.6 = 180

A = 58.5

Using the values, in the law of sines, we get:

[tex]\frac{943}{sin(58.5)} = \frac{c}{sin(18.6)}\\\\ c = \frac{943 \times sin(18.6)}{sin(58.5)}\\\\ c = 352.8[/tex]

Thus, the measure of side AB would be 352.8 feet

Answer:

The length of AB is 352.8 feet

Step-by-step explanation:

* Lets revise some facts to solve the problem

- The sine rule: [tex]\frac{sinA}{BC}=\frac{sinB}{AC}=\frac{sinC}{AB}[/tex]

- The sum of the measures of the interior angles of a triangle is 180°

* Lets solve the problem

- In Δ ABC

∵ m∠ B = 102.9°

∵ m∠ C = 18.6°

∵ m ∠A + m∠ B + m∠ C = 180° ⇒ interior angles of a Δ

∴ m ∠A + 102.9 + 18.6 = 180

∴ m ∠A + 121.5 = 180 ⇒ subtract 121.5 from both sides

∴ m∠A = 58.5°

* Lets use the sine rule to find AB

∵ BC = 943

∵ m∠A = 58.5°

∵ m∠ C = 18.6°

∴ [tex]\frac{sin(58.5)}{943}=\frac{sin(18.6)}{AB}[/tex]

- By using cross multiplication

∴ AB × sin(58.5) = 943 × sin(18.6)

- Divide both sides by sin(58.5)

∴ AB = [943 × sin(18.6)] ÷ sin(58.5) = 352.76 ≅ 352.8

* The length of AB is 352.8 feet

Answer:

49

Step-by-step explanation:

I think I have read this right!

You let me know if you did not mean to write the following:

[tex]\sum_{k=1}^{7}(1+(k-1)(2)[/tex]

Alright so the lower limit is 1 and the upper limit is 7.

All this means is we are going to use the expression 1+(k-1)(2) and evaluate it for each natural number between k=1 and k=7 and at both k=1 and k=7.

The sigma thing means we add those results.

So let's start.

Evaluating the expression at k=1: 1+(1-1)(2)=1+(0)(2)=1+0=1.

Evaluating the expression at k=2: 1+(2-1)(2)=1+(1)(2)=1+2=3.

Evaluating the expression at k=3: 1+(3-1)(2)=1+(2)(2)=1+4=5.

Evaluating the expression at k=4: 1+(4-1)(2)=1+(3)(2)=1+6=7.

Evaluating the expression at k=5: 1+(5-1)(2)=1+(4)(2)=1+8=9.

Evaluating the expression at k=6: 1+(6-1)(2)=1+(5)(2)=1+10=11.

Evaluating the expression at k=7: 1+(7-1)(2)=1+(6)(2)=1+12=13.

Now for the adding!

1+3+5+7+9+11+13

  4+  12+    20+13

        16+     33

           49

Answer:

√3 - 2.

Step-by-step explanation:

Let A = 330 degrees so  A/2 = 165 degrees.

tan A/2 = (1 - cos A) /  sin A

tan 165 = (1 - cos 330) / sin 330

= (1 - √3/2) / (-1/2)

=  -2(1 - √3/2)

= -2 + 2 * √3/2

=  √3 - 2.

Answer:

[tex]\sqrt{3}[/tex] - 2

Step-by-step explanation:

Using the half- angle identity

tan( [tex]\frac{x}{2}[/tex] ) = [tex]\frac{sinx}{1+cosx}[/tex]

[tex]\frac{x}{2}[/tex] = 165° ⇒ x = 330°

sin330° = - sin30° = - [tex]\frac{1}{2}[/tex]

cos330° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

tan165° = [tex]\frac{sin330}{1+cos330}[/tex]

            = [tex]\frac{-\frac{1}{2} }{1+\frac{\sqrt{3} }{2} }[/tex]

            = - [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{2+\sqrt{3} }[/tex]

            = - [tex]\frac{1}{2+\sqrt{3} }[/tex]

Rationalise by multiplying numerator/ denominator by the conjugate of the denominator

The conjugate of 2 + [tex]\sqrt{3}[/tex] is 2 - [tex]\sqrt{3}[/tex], hence

tan 165°

= - [tex]\frac{2-\sqrt{3} }{(2+\sqrt{3})(2-\sqrt{3})  }[/tex]

= - [tex]\frac{2-\sqrt{3} }{4-3}[/tex]

= - (2 - [tex]\sqrt{3}[/tex] )

= - 2 + [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] - 2

Answer:

Part 1) The area of the structure is [tex]2,453.25\ ft^{2}[/tex]

Part 2) The slab will contain  [tex]1,226.625\ ft^{3}[/tex] of cement

Step-by-step explanation:

Part 1) Find the area of the structure

we know that

The area of the structure is equal to the area of rectangle plus the area of semicircle

Find the area of rectangle

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]L=70\ ft[/tex]

[tex]W=30\ ft[/tex]

substitute

[tex]A=(70)(30)[/tex]

[tex]A=2,100\ ft^{2}[/tex]

Find the area of semicircle

The area of semicircle is

[tex]A=\frac{1}{2}\pi r^{2}[/tex]

we have

[tex]\pi =3.14[/tex]

[tex]r=15\ ft[/tex]

substitute

[tex]A=\frac{1}{2}(3.14)(15)^{2}[/tex]

[tex]A=353.25\ ft^{2}[/tex]

Find the area of the structure

Adds the areas

[tex]A=2,100+353.25=2,453.25\ ft^{2}[/tex]

Part 2) If the structure is 6 in thick, how many cubic feet of cement will the slab contain?

Remember that

[tex]1\ foot=12\ inches[/tex]

Convert inches to feet

[tex]6\ in=6/12=0.5\ ft[/tex]

Find the volume of the structure

To obtain the volume , multiply the area by 0.5 ft (thick)

so

[tex]V=2,453.25*0.5=1,226.625\ ft^{3}[/tex]

Answer:

Johnny

Step-by-step explanation:

I don't think you put the whole question out

Answer:

B: 12.2cm

Step-by-step explanation:

Got it right on edge 2021✅

Answer:

8

Step-by-step explanation:

To find Y, find X first. Multiply 2 by W (3) which is 6, and divide by 3, which gives us X=2. The inequality W+Z=X+Y substituted is 10=2+Y. Subtract 2 from 10 and you get Y=8

Answer:

13) 8

14) 2X  or 4W/3 (depending on what the choices are)

Step-by-step explanation:

So I'm using the box given:

If                                 then

W  X                            W+Z=X+Y and 2W=3X

Y    Z

13)

3   X                           3+7=X+Y and 2*3=3*X

Y   7

To get W,X,Y, and Z I compared it to the first lay out and then replace the other W's,X's,Y's, and Z's.

So we have 3+7=X+Y which means 10=X+Y.

We also have 2*3=3*X which means 2=X (I divided both sides by 3).

If X=2 then 10=X+Y gives us 10=2+Y.

10=2+Y can be solved by subtracting 2 on both sides:

8=Y

Y=8

14)

W  X                                  W+W=X+Y and 2W=3X

Y   W

So W+W=X+Y means 2W=X+Y

We are also given 2W=3X which means by substitution into the first equation we get 3X=X+Y.

3X=X+Y can be solved by subtracting X on both sides:

2X=Y

We can also write Y in terms of W.

We have 2W=3X so that means X=2W/3 (I divided both sides by 3)

Now I'm going to replace X in 2X=Y with (2W/3) giving me:

2(2W/3)=Y

4W/3=Y

Answer:

Step-by-step explanation:

Firstly you must understand you want to get the value of  y.

So put in values into equation which make x.

To understand here lets look at  y = 0

if y is to be 0 then x is 3.

If we substitute this value into equation (B) we get the result.

Now we have identified our answer, all is left is to substitute all other values of x and see if y are true.

So , we can see B is the answer

Answer: B

Step-by-step explanation:

The answer has to be either A, or B, because when x input is negative, the y input is positive. Visa versa.

Then just input x and y into the equation to see which answer is correct.

First let’s do A: 12=-2(-3)-6

12=6-6

12 doesn’t equal 0, so A is incorrect

So then B is the obvious solution, but let’s solve it to make sure: 12=-2(-3)+6

12=6+6

This equation is true, so the answer is B

Answer:

Step-by-step explanation:

CPCTC: Corresponding Parts of Congruent Triangles are Congruent

If ΔLMN ≅ ΔXYZ, then:

B. LN ≅ XZ

C. ∠Y ≅ ∠M

E. MN ≅ YZ

Corresponding sides:

LN → XZ

LM → XY

MN → YZ

Corresponding angles:

∠L → ∠X

∠N → ∠Z

∠M → ∠Y

Answer:

C. MN=YZ; D. LN=XZ; and F. Y= M