These triangles are congruent by the triangle congruence postulate:

**Answer:**

SAS

**Step-by-step explanation:**

SAS is side, angle, side so two sides are congruent and one angle is congruent.

If you look at the picture the side that is shared by both triangles is equal.(side)

The two sides with the line through them means they're equal.

(side)

The picture shows the two angles are equal.

(angle)

=SSA or SAS

Solve for s.

19.1 = s − –7.3

s =

If 7.3 is a negative, s = 11.8. If 7.3 isn’t, s = 26.4.

Make sure when you have negatives, most of the time you add parentheses. An example is (-5).

Make sure when you have negatives, most of the time you add parentheses. An example is (-5).

the first one please help!!

The y-intercept of f(x) is **equal to** the y-intercept of g(x).

the** y-coordinate** of a point on a surface, curve, or line where they cross the** y-axis.**

Finding the value of y at **x=0 **will help you locate the **y-intercept** on a graph. The graph's **intersection** with the y-axis occurs here.

When the **slope** of the line being studied is known, and the provided point is also the** y - intercept**, the slope intercept formula,** y = mx + b**, is utilized** (0, b)**. B is used in the equation to indicate the y value of the y intercept point.

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Help me please someone this is very confusing to me.

**Answer:**

7

**Step-by-step explanation:**

slope = rise/run = (difference in y)/(difference in x)

First, we find a difference in y.

Subtract any two values of y.

For example: 35 - 14 = 21

Now we find the corresponding difference in x.

Now subtract the x values corresponding to those y values in the same order.

-1 in x corresponds to 35 in y.

-4 in x corresponds to 14 in y.

That means your difference in x is the subtraction -1 - (-4) = -1 + 4 = 3

The difference in y is 21.

The difference in x is 3.

slope = (difference in y)/(difference in x) = 21/3 = 7

Answer: 7

Something's Strange about this little problem..

99 + 2 = ?

**Answer:**

the answer is 101 !!!

There's isn't nothing strange your just over thinking it!

101! :D

Trust your gut, thanks for the points :)

Have a good night !!

Trust your gut, thanks for the points :)

Have a good night !!

I need help with this question please

**Answer:**

x=-4.5 x=-0.5

y=-1

vertex=-2

A rectangle is 32ft by 8ft. Stephanie dilated the rectangle and the dimensions of the image were 24ft by 6ft. What was the scale factor used?

**Answer:4**

**Step-by-step explanation:**

image dimension = 24 by 6 feet

preimage dimension = 32 by 8 feet

so 24/6 = 32/8 = 4

scale factor = 4

PLEASE HELP IM BEGGING

**Answer:**

y= 3/2 x + -4

**Step-by-step explanation:**

-4 Is the y intercept (the vertical axis)

the 3/2 is the rise over run of the line (how many up over how many across). It's positive because of the slope up to the right.

A Curve has the equation y=kx^2 +1 And a line has the equation y=kx where

K is a

non-zero

Constant

1)Find the Set

the value of k

for which the

curve and line have no common point.

(1) state the value for which the line is a

tangent to the Curve and for this case, find the coordinates

of the point where the line

touches the curves

The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).

The value for which the line is a **tangent **is k = 4.

The coordinates of the point where the line touches the curves is point of **tangency **= ( 1/2 , 2).

**What is tangent?**

**Tangents **in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.

Given equations in the question:

y = kx² + 1

y = kx

Equating y

kx² + 1 = kx

kx² -kx + 1 = 0

This is **Quadratic equation** is of the form ax²+bx+c=0 where a , b and c are real also a≠0.

D = b²-4ac is called **discriminant**.

and we know that,

D >0 roots are real and distinct

D =0 roots are real and equal

D < 0 roots are imaginary ( not real ) and different

For no common solution D < 0

For **tangent **D = 0

so,

kx² -kx + 1 = 0

D = (-k)² - 4k = k² - 4k = k(k - 4)

k(k - 4) < 0

if 0 < k < 4

Hence values of k for which the curve and the line have no common points is **k ∈ (0 , 4)**.

for **tangent**

k(k - 4) = 0

k is non zero

Hence **k = 4**

After putting the value of k, given equations are:

y = 4x² + 1

y = 4x

solving these equations to get value of x and y:

4x² + 1 = 4x

4x² - 4x + 1 = 0

(2x - 1)² = 0

x = 1/2

y = 2

**Point of tangency = ( 1/2 , 2)**

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For a project in her Geometry class, Mila uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.45 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.2 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

The **goalpost** is 15.13 meters **tall** which is labeled as X in the **figure** which has been attached below.

She walks 13.45 meters away from the **goalpost**, then places a **mirror** flat on the ground with an X in the **center**. She next walks 1.2 meters to the **opposite** side of the mirror, where she can easily see the top of the goalpost depicted in the X. Her partner determines that the **distance** between her eyes and the ground is 1.35 meters.

The **ratio** is defined as a relationship between two quantities, it is expressed as one **divided **by the other.

As per the given information, the **figure** has been attached below.

Set up the **proportional** and solve for x

1.2 : 13.45 = 1.35 : x

⇒ 1.2 / 13.45 = 1.35 / x

Cross **multiplication**, and we get

⇒ 1.2x = 1.35 × 13.45

**Divided** by 1.2 into both sides of the above equation,

⇒ x = (1.35 × 13.45) / 1.2

⇒ x = 15.13

Therefore, the **goalpost** is 15.13 meters **tall**.

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MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH LOOK AT PHOTO

The **percentage** of** students **that use **other means** to travel school is **24%**

Percentage is the** ratio** of the **number** for which you want to find percentage to the **total number** with which you want to compare or out of and multiply this ratio with 100.

percentage = (**part** /** whole**) ×100

Given that a school has** 825 total** students.

**Percentage** of students travelling by** car** = 20%

**Percentage** of students travelling by** bus** = 48%

**Percentage** of students travelling by** bicycle** = 8%

Number of students travelling by car = 20% of 825 = (20/100)×825 = 165

Number of students travelling by bus = 48% of 825

= (48/100)×825 = 396

Number of students travelling by bus = 8% of 825 = (8/100)×825 = 66

**Number** of **students** travelling by **other means** = 825-165-396-66 = **198**

Therefore, the **Percentage** of** students** travelling by** other means** = (198/825) ×100 =** 24**%

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graph this function f(x) = 1/4(x) - 7

**Answer:**

This is your graph to the following equation f(x) = 1/4(x) - 7

This is f(x)=1/4(x)-7 when graphed

A floor plan of an apartment has a rectangular living room. Its length is 10 centimeters and its width is 4 centimeters. The scale of the floor plan diagram is 2 centimeters for every 1 meter. What is the actual area of the apartment's living room?

The **actual area** of the apartment's living room is 10 [tex]m^{2}[/tex]

Given

Room is in the shape of a** rectangle**

Length of the room (L)= 10 cm

Width of the room (W) = 4 cm

Also the scale of floor plan is 2 cm for every 1 meter

Initially the are of the living room = **area of rectangle**

Area of the rectangle = length × width

= 10 × 40

= 40 [tex]cm^{2}[/tex]

To find actual floor area we need to** scale the dimensions**

Since 2cm = 1 m

10cm = 5m and 4 cm = 2m

Now calculating the actual area

Area = length × width

= 5×2

=10 [tex]m^{2}[/tex]

Hence the **actual area** of the living room is 10 [tex]m^{2}[/tex]

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Write the fraction 622/1000 in its simplest form

Answer:

311/55

Step-by-step explanation:

i devided each by 2 and got this then i looked it up and it said this so id k

hope this helped

I need help................

**Answer:**

D

**Step-by-step explanation:**

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (1, 7) ← 2 points on the line

m = [tex]\frac{7-1}{1-(-2)}[/tex] = [tex]\frac{6}{1+2}[/tex] = [tex]\frac{6}{3}[/tex] = 2

use either of the 2 points on the line

using (- 2, 1 ) , then

y - 1 = 2(x - (- 2) ) , that is

y - 1 = 2(x + 2) ← equation in point- slope form

Given f(x) = x3 – 2x2 – x + 2, the roots of f(x) are ✔ –1, 1, 2 . Determine the end behavior of f(x).

**Answer:**

1, -1 and 2

**Step-by-step explanation:**

The zeros of the given polynomial function are 1, -1 and 2

Given the polynomial function

First, we need to assume a value of x to check if it will give us zero after substituting:

Assuming x = 1

Since f(1) =0, hence x - 1 is a factor

Dividing x - 1 by the given polynomial function, we will have:

Equating the result to zero

x + 1 = 0 and x - 2 = 0

x = -1 and 2

Hence the zeros of the given polynomial function are 1, -1 and 2

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A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?

The **equation** which is useful to find the **amount **in **gallons** of water to the number of **minutes** since **filling started **is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water.

Determine the **known** quantities and designate the **unknown **quantity as a variable while trying to **set up** or **construct** a linear equation to fit a real-world **application**.

The amount of water **initially** in the **trough **= 25 gallons.

The **rate **of **adding **water = 11 gallons per minute

Therefore, the **total amount **(A) of water in x minutes will be,

A = 25 + 11x

The **number **of **minutes **to have 80 gallons of water is,

80 = 25 + 11x

11x = 55

x = 5 minutes.

Hence "The **equation** which is useful to find the **amount **in **gallons** of water to the number of **minutes** since **filling started **is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water".

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Please Help me turn vertex form to standard form!!

**Answer:**

See below

**Step-by-step explanation:**

y = -(x-1)^2 +4 Expand R side

y = - ( x^2 -2x+1) + 4

y = -x^2 +2x -1 + 4

y = -x^2 + 2x + 3 a = -1 b = 2 c = 3

Simple Interest Round answers to the nearest cent. 1. John is going to invest $100 in an account for 3 years. If the account earns 6% simple interest, how much interest can he expect to earn?

Given Data:

The initial investment is: P=$100

The total period of investment is: t=3

The annual interest is: 6%.

For the simple interest, the expression to calculate the interest in t years is,

[tex]I=(P\times\frac{r}{100})\times t[/tex]Here r is in percentage.

Substitute known values in the above expression.

[tex]\begin{gathered} I=(100\times\frac{6}{100})\times3 \\ =(6)\times3 \\ =18 \end{gathered}[/tex]Thus, the total intrest for 3 years will be $18.

In Barangay San Jose, it was found that the population double every 10 years. If in the year 1995, the population was 7824, what will be the population in the year 2015?

The** population** in the** year 2015 is 31296.**

In 1995 the population was 7824. It was found that the population gets double every 10 years.

We have to find the population in the year 2015.

Rate = 200% = 2

Time =( 2015 - 1995) / 10

= 20/10

= 2

The **population in 2015 **= population in 1995 ×[tex]rate^{time}[/tex]

= 7824 × [tex]2^{2}[/tex]

= 7824 × 4

= 31296

Therefore the** population in the year 2015 is 31296.**

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PLEASE HELP. Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. 1. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. 2. Describe how you would graph this line using the slope-intercept method. Be sure to show all your work. 3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to show all your work. 4. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. 5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.

They are similar because they have the same** slope the equation** is

y = -2/3x + 531

**What is in slope-intercept form?**

changing 2x+3y=1470 to slope intercept form is solving for y

minus 2x both sides and divide by 3

y = -2/3x + 490

the slope is -2/3

the y intercept is y=490 or the point (0,490)

to graph it, I would start at the origin and go up 490 units on the y axis and put a point there

then go -2 units up (2 down) and 3 to the right and put a point there

then connect the 2 points with a line

in function notation, replace y with f(x) to get

y = -2/3x + 490

graph below

intercepts labeled

2x+3y=1593

they are similar because they have the same slope

the equation is y = -2/3x + 531

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is 15 feet above sea level negative or positive or a zero

**Answer:**

Positive

**Step-by-step explanation:**

Below sea level would be negative and at sea level would be zero.

positive. above is positive, below is negative :)

Surface Area from a Net

He used 647.75 square meters of wrapping **paper** to wrap the gift.

According to the question,

We have the following information:

We have a figure made of 2 same triangles and 3 rectangles with different measurements.

Area of triangle = 1/2 * base*height

Area of triangle = (1*7*14)/2

Area of triangle = 49 [tex]m^{2}[/tex]

Now, the area of another same **triangle** will also be 49 [tex]m^{2}[/tex].

Now, we have:

Area of upper rectangle = length*breadth

Area of upper rectangle = 15*14

Area of upper rectangle = 210 [tex]m^{2}[/tex]

Area of middle **rectangle** = length*breadth

Area of middle rectangle = 15*7

Area of middle rectangle = 105 [tex]m^{2}[/tex]

Area of lower rectangle = length*breadth

Area of lower rectangle = 15.65*15

Area of lower rectangle = 234.75 [tex]m^{2}[/tex]

Now, the area of the wrapping paper will be the** sum** of all of these areas.

Area of paper = Area of 2 triangles + area of upper rectangle + area of middle rectangle + area of lower rectangle

Area of paper = 49+49+210+105+234.75

Area of paper = 647.75 [tex]m^{2}[/tex]

Hence, the area of wrapping paper is 647.75 [tex]m^{2}[/tex].

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What is 6.849 times ten to the fourth power minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 decimal places.

the answer in scientific notation rounding to 2 **decimal **places is given by 68490.98

**power **minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 **decimal **places.

6.849 *(10)^4=6.849* 10000=68490

2.329*(10)^-2= 0.02329

according to the question

6.849 times ten to the fourth power minus 2.329 times ten to the negative second **power**

therefore 68490-0.02329

=68489.9767

round to 2 decimal

the answer in scientific notation rounding to 2 **decimal **places is given by 68490.98

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x³-10x = 100

Use a trial and improvement method to find this solution.

Give your answer correct to 1 decimal place.

You must show all your working out

The value of x is **approximately** 5.4 when x^3 -10x = 100

**How to solve the equation?**

The equation is given as:

x^3 -10x = 100

**Using trial **by error, we keep testing for the value of x that is true for x^3 -10x = 100

After **several** attempts, we have:

x = 5.4 (approximately)

Substitute 5.4 for x in x^3 -10x = 100

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100This means that x is approximately 5.4 when x^3 -10x = 100

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The length of a base of a rectangular prism is 12 dm and the width is 5 dm. What should be the height of the rectangular prism be so that it's volume is smaller than the volume of a cube with a side of 9 dm? (for 30 points) will give you brainlyiest or smthing title

**Answer:**

Must be less than 12.15 dm

**Step-by-step explanation:**

The concession stand are the football games are 288 customers. Those customers, about 77% bought a hot dog. About how many customers buy a hotdog?

Fueron 221 clientes

288/100%= 288

2.88x77%= 221

288/100%= 288

2.88x77%= 221

An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin

The **percentage **20% of the **costs **y is given as 0.20y thus the **expression **which represents the **price **of the item after the **discount **is P = y - 0.20y.

The **percentage** is just like the **amount** of that value but between 1 to 100 and it is very **useful **to **predict **for example if you say 678 then we have to know about the full **number **also but if you say 80% then it **becomes clear**.

It is known that x% of something y is given as,

x% of y = (x/100)y

Given that **discount **of 20% of y

20% of y = (20/100)y

20% of y = 0.20y

Now the **final** price = **initial **price - **discount **

Final price (P) = y - 0.20y

Hence"The **percentage **20% of the **costs **y is given as 0.20y thus the **expression **which represents the **price **of the item after the **discount **is P = y - 0.20y".

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Can I have some help with the question in the attachment. I've done (a) but I think I'm doing (b) wrong

**Answer:**

8.33

**Step-by-step explanation:**

He has to be at work by 10:30, but it takes 20 mins to walk

So, 10:30-20 minutes=10:10

We then look at the arrival time closest to this, which would mean he would arrive at 10.06.

trace this back the bus would gett him at 8:38, but its a 5min walk.

8:38-5 minutes+8.33

hope this helps :)

How do you proof that sqrt(2) is irrational?

I tried this,

p/q = sqrt(2)

p^2/q^2=2

p^2=2q^2

let p = q * sqrt(2) , (equation from top one)

(q*sqrt(2))^2=2q^2

2q^2=2q^2,

q=q

Is anything wrong or does this also prove that sqrt(2) is irrational, if so how?

Assume √2 is rational, so

√2 = p/q

for some relatively prime integers p,q - meaning we can't reduce p/q any further - and q ≠ 0.

Then

p = √2 q

and squaring both sides gives

p² = 2q²

This tells us that p² is even, so 2 divides p². But if 2 divides p², it must also divide p, since p is a square number. So p = 2r for some integer r, and we have

(2r)² = 2q²

4r² = 2q²

2r² = q²

We're in the same situation as before - 2 divides q², so 2 divides q. Both p and q are thus divisible by 2, but this contradicts our assumption that p and q are relatively prime, which means √2 cannot be expressed as a rational number p/q. Therefore √2 is irrational.

What you've written in your proof is technically correct, but it doesn't help in the irrationality proof.

-3x+7=-x-1

Simplify and solve for the variable

-3x+7=-x-1

+3x +3x

7=2x-1

+1 +1

8=2x

8/2

X=4

+3x +3x

7=2x-1

+1 +1

8=2x

8/2

X=4

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