Which triangles must be congruent?
A. AABC, AFDE, and AGIH
B. AABC and AFDE only
C. AGIH and AABC only
D. none of the triangles​

Answer:

[tex]x=-3\ or\ \frac{5}{2}[/tex]

Step-by-step explanation:

Given:

Given equation is.

[tex]2x^{2} +3x-10=2x+5[/tex]

Find values of x?

Solution.

[tex]2x^{2} +3x-10=2x+5[/tex]

[tex]2x^{2} +3x-10-2x-5=0[/tex]

[tex]2x^{2} +x-15=0[/tex]

Find the roots of the equation.

compare the above equation with [tex]ax^{2} +bx+c=0[/tex]

Therefore, [tex]a=2,b=1,c=-15[/tex]

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

Put a,b and c value in above equation.

[tex]x=\frac{-1\pm\sqrt{(1)^{2}-4(2)(-15)}}{2(2)}[/tex]

[tex]x=\frac{-1\pm\sqrt{1-8(-15)}}{4}[/tex]

[tex]x=\frac{-1\pm\sqrt{1+120}}{4}[/tex]

[tex]x=\frac{-1\pm\sqrt{121}}{4}[/tex]

[tex]x=\frac{-1\pm\sqrt{(11)^{2}}}{4}[/tex]

[tex]x=\frac{-1\pm 11}{4}[/tex]

For positive sign

[tex]x=\frac{-1+ 11}{4}[/tex]

[tex]x=\frac{10}{4}[/tex]

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

For negative sign

[tex]x=\frac{-1- 11}{4}[/tex]

[tex]x=\frac{-12}{4}[/tex]

[tex]x=-3[/tex]

[tex]x=-3\ or\ \frac{5}{2}[/tex]

Therefore, the value of [tex]x=-3\ or\ \frac{5}{2}[/tex] satisfy the given equation.

Answer:

x = 4

Step-by-step explanation:

f(x) = I  x+1 I ​

when x = -5

f(-5) = I  (-5) +1 I

= I  -5+1 I ​

= |-4|

= 4

Answer:

substitute x for -5

f(-5)=|-5+1|

f(-5)=|-4|

however, absolute value is the distance from 0 and so is always positive since you cannot have negative distance.

so f(-5)=4

Answer:

the answer is 1

Step-by-step explanation:

X1=3 X2=7

Y1=-2 Y=r

M=y2-Y1/X2-X1

3/4=r-(-2)/7-3

3/4=r+2/4

Cross multiply

4(r+2)=4*3

4r+8=12

collect like terms

4r=12-8

4r=4

divide the by the co efficient of x

r=1

To find the missing coordinate “r” given two points on a line and the slope, we can use the slope formula. Using the given slope and the coordinates of the points, we can set up an equation to solve for the missing value of “r”. By solving the equation, we find “r” is equal to 1.

To find the missing coordinate r, we can use the slope formula. The slope m is given as 3/4, and the coordinates of the two points are (3, -2) and (7, r).

We can use the formula: m = (y2 - y1) / (x2 - x1) to find the missing value of r. Substituting the values, we have:

3/4 = (r - (-2)) / (7 - 3)

Solving for r:

3/4 = (r + 2) / 4

Multiplying both sides by 4:

3 = r + 2

Subtracting 2 from both sides:

r = 1

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Answer & Explanation:

To determine the age of a tree, first find its diameter by measuring the circumference of the trunk in inches and then dividing that number by pi. Once you have the tree's diameter, look up the growth factor for the type of tree you're measuring, which is how much width it gains annually.

The height and diameter of a tree is a function of its age.

Growth rate of a system is defined as the rate at which the system grows by length, breadth, height, etc.

Here,

The growth rate of a tree represents the age of the tree. The measurement of the height and diameter of the tree is used to calculate the age of the tree. These measurements of height and radius of the tree can be considered as a function of its age.

The method of calculating the age of the tree is,

The circumference at a height above 4.5 feet from the ground is measured(breast height).

Dividing the circumference at breast height with pi(3.14), thus we get the diameter at breast height.

Multiplying the diameter with growth factor will give the age of the tree in years.

Hence,

The height and diameter of a tree is a function of its age.

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Answer:

see explanation

Step-by-step explanation:

(a)

f(0)

Since x = 0 < 5, then

f(0) = x + 4 = 0 + 4 = 4

(b)

f(6)

Since x = 6 meets the condition 5 ≤ x < 7, then

f(6) = 8

Answer: Tracey attended 70% of the basketball games.

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

As a fraction, 14 / 20.

If you multiply the 2 Terms by 5, you would get 70 / 100 which equals 70%.

Best of Luck!

Answer:

The amount into account after a year is $1042

Step-by-step explanation:

Given as :

The principal amount into the account = p = $1000

The amount is growing at the rate = r = 4.2 % per year

Let The Amount into account after 1 year = $A

So, According to question

The amount into account after 1 year = The principal amount × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm 1}[/tex]

Or, A = $1000 × [tex](1+\dfrac{\textrm 4.2}{100})^{\textrm 1}[/tex]

Or, A = $1000 × 1.042

Or, A = $1042

So, The amount into account after a year =  A = $1042

Hence,The amount into account after a year is $1042 . Answer

Answer:

[tex]7\dfrac{1}{9}\ m^2[/tex]

Step-by-step explanation:

If the length of the square side is a units, then the area of the square is

[tex]A=a^2\ un^2.[/tex]

In your case, the side length is

[tex]a=2\dfrac{2}{3}\ m,[/tex]

then the area is

[tex]A=2\dfrac{2}{3}\cdot 2\dfrac{2}{3}\\ \\ \\A=\dfrac{2\cdot 3+2}{3}\cdot \dfrac{2\cdot 3+2}{3}\\ \\ \\A=\dfrac{8}{3}\cdot \dfrac{8}{3}\\ \\ \\A=\dfrac{64}{9}\\ \\ \\A=7\dfrac{1}{9}\ m^2[/tex]

Answer:

2x(x + 5)(x - 2y)

Step-by-step explanation:

Given

2x³ + 10x² - 4x²y - 20xy ← factor out 2x from each term

= 2x(x² + 5x - 2xy - 10y)

Factor the first/second and third/fourth terms inside the parenthesis

= 2x(x(x + 5) - 2y(x + 5)) ← factor out (x + 5) from each term in the parenthesis

= 2x(x + 5)(x - 2y)

Answer:

Domain and range of the equation

Y = 3X-7.25

will be Set of all Real numbers.

Step-by-step explanation:

Because at any value of x, you will get a respective value of y. For example if you put X=0, then y=7.25. You can put any value of X in the equation and for each value equation will be true and will give respective value of y.

518x5=2,590, So your estimate is about 2,600, Because we want to round up, So we look in the tens place and we see a nine, so that means we go up on, Also 5 and up means we gonna round up and 5 and below means we gonna round down.

The answer to 518*5 is 2590 or rounded, 3000, or 2600.

You can get your answer my multiplying 518 by 5 and rounding it to the nearest thousands place, hundreds place or tens place.

Hope this helped!

Answer:

263.76

Step-by-step explanation:

To answer this question, we need to know the equation for surface area of a cylinder which can be given as Surface Area=2*pi*[tex]R^{2}[/tex]+2*pi*R*H, where R is the radius of the cylinder (also can be calculated as Diameter/2=6/2=3) and H is the height of the cylinder which is given as 11. Considering pi=3.14, the surface area of the cylinder can now be calculated as 2*3.14*[tex]3^{2}[/tex]+2*3.14*3*11=263.76.

Answer:

All the right triangles will be similar.

Step-by-step explanation:

See the attached diagram.

Let us assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.

Since the slope of the line OP is constant and assume that it makes x° with the positive x-axis.

Hence, [tex]\tan x = \frac{AC}{BC} = \frac{A'C'}{B'C'}[/tex]

⇒ [tex]\frac{AC}{A'C'} = \frac{BC}{B'C'}[/tex]

Therefore, the sides of the two right triangles are in the same ratio and hence, Δ ABC and Δ A'B'C' are similar.

Hence, all the right triangles will be similar. (Answer)

The cost of one book is $6.

Step-by-step explanation:

Given,

Lizzie paid for 8 books = $50 bill

Alex paid for 3 books = $20 bill

As the both received same change.

Let,

x represent cost of one book.

y represent the change received.

According to given statement;

50-8x=y    Eqn 1

20-3x=y    Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]20-3x=50-8x\\-3x+8x=50-20\\5x=30[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{30}{5}\\x=6[/tex]

The cost of one book is $6.

Keywords: linear equation, substitution method

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Answer:c

Step-by-step explanation:

Answer:

Step-by-step explanation:

C

Answer:

!. [tex]\displaystyle 23[/tex]

Step-by-step explanation:

Use the Distance Formula:

[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[15 - 15]^2 + [-20 - 3]^2} = \sqrt{0^2 + [-23]^2} = \sqrt{0 + 529} = \sqrt{529} = 23[/tex]

Since we are talking about distance, we ONLY want the NON-NEGATIVE root.

I am joyous to assist you anytime.

Answer:

23%

Step-by-step explanation: ???

Final answer:

Tommy's class collected $8.00.

Explanation:

To find out how much money Tommy's class collected, we can set up an equation:

x * 2 = 16.00

Solving for x, we divide both sides of the equation by 2:

x = 8.00

Therefore, Tommy's class collected $8.00.

Final answer:

The units digit is 0, the hundreds digit is 4, and the tens digit is 8, making the 3-digit number 480.

Explanation:

The question involves finding a 3-digit number where the hundreds digit is four more than the units digit, the tens digit is twice the hundreds digit, and the sum of the digits is 12. To solve this, we can use algebra.

Let's designate the units digit as 'u'. According to the problem, the hundreds digit will then be 'u + 4'. The tens digit is twice the hundreds digit, which gives us '2(u + 4) = 2u + 8'. Now we can use the information that the sum of the digits equals 12 to create the equation: u + (u + 4) + (2u + 8) = 12.

Simplifying this equation, we get: 4u + 12 = 12, which further reduces to 4u = 0. This indicates that u, the units digit, is 0. Thus, the hundreds digit is 0 + 4 = 4 and the tens digit is 2×4 = 8.

The 3-digit number we are looking for is therefore 480.

Answer:

$280

Step-by-step explanation:

Principal = $3,500

Time = 2 Years

Interest Rate = 4%

Interest = Principal x Time x Interest Rate

Interest = $3,500 x 2 x 0.04

Interest = $280

B clearly because u would substitute the x and y with the ordered pairs

Answer:

Step-by-step explanation:

Final answer:

To find the weight of the bar of gold, solve the equation (1/3)x + 30 = x, where x represents the weight of the bar. After simplifying, the weight of the bar is found to be 45 pounds.

Explanation:

To solve this problem, let's assume the weight of the bar of gold is x pounds. According to the given information, one-third of the weight of the bar of gold plus 30 pounds equals the weight of the bar of gold. This can be written as:

(1/3)x + 30 = x

To solve for x, we can start by subtracting (1/3)x from both sides of the equation:

(1/3)x + 30 - (1/3)x = x - (1/3)x

This simplifies to:

30 = (2/3)x

To isolate x, we can multiply both sides of the equation by 3/2:

(3/2)(30) = (3/2)(2/3)x

45 = x

Therefore, the bar of gold weighs 45 pounds.

Answer: m = 7/4

Step-by-step explanation: Use the slope formula to find the slope m.

Hope this helps you out! ☺

Answer:

7/4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-3-4)/(-3-1)

m=-7/-4

m=7/4

Answer:

The statement is true

The lines are perpendicular

Step-by-step explanation:

we have

[tex]x=4[/tex] ----> equation A

The equation A represent a vertical line (is parallel to the y-axis)

The slope is undefined

[tex]y=5[/tex] ----> equation B

The equation B represent a horizontal line (is parallel to the x-axis)

The slope is equal to zero

Remember that

The y-axis and the x-axis are perpendicular lines

so

Line A and line B are perpendicular lines too

therefore

The statement is true

Complete the equation of the line whose slope is -2 and y intercept is (0,3)

The equation of the line whose slope is -2 and y intercept is (0,3) is y = -2x + 3

Given that line has slope of -2 and y - intercept of (0, 3)

We have to find the equation of line

The equation of line can be found by using the slope intercept form

The slope intercept form is given as:

y = mx + c

Where "m" is the slope of line and "c" is the y-intercept

Here given that slope = m = -2

y - intercept is the y-coordinate of a point where a line intersects the y-axis.

So here y intercept is (0, 3) and we get c = 3

Substituting the values in slope intercept form we get,

y = -2x + 3

Thus the equation of line is found

Answer: 1,350 hats

Step-by-step explanation: First, it's important to understand that 50% is equivalent to the fraction 1/2.

So, the next year that hat store will sell 1/2 more hats.

First, we need to divide 900 by 2 which gives us 450.

Now, we simply add 450 to to the number of hats the store sold the first year.

450 + 900 = 1,350

This means that the hat store will sell 1,350 hats the next year.

Answer: [tex]2 z + 6[/tex] and [tex]2 (z + 3)[/tex]

Step-by-step explanation:

We have te following expression:

[tex]z+(z+6)[/tex]

Which can be written as:

[tex]z+z+6=2z+6[/tex]

Applying common factor 2 in the right side of the equation:

[tex]z+z+6=2(z+3)[/tex]

Answer:

The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7  

Step-by-step explanation:

Given as :

The points as [tex]x_1[/tex] = 6

And [tex]y_1[/tex] = - 3

The slope of the line = m = [tex]\dfrac{2}{3}[/tex]

Now, The equation of line in slope-point form

y -  [tex]y_1[/tex] = m × (x -  [tex]x_1[/tex])

Or, y - (-3) =  [tex]\dfrac{2}{3}[/tex] × (x - 6)

Or, y + 3 =  [tex]\dfrac{2}{3}[/tex] × (x - 6)

Or, 3 × (y + 3) = 2 × (x - 6)

Or, 3 y + 9 = 2 x - 12

Or, 3 y = 2 x - 12 - 9

Or, 3 y = 2 x - 21

∴  y = [tex]\dfrac{2}{3}[/tex] x - [tex]\dfrac{21}{3}[/tex]

i.e y = [tex]\dfrac{2}{3}[/tex] x - 7

So, The equation of line = y = [tex]\dfrac{2}{3}[/tex] x - 7

Hence, The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7  Answer

Radian measure of the central angle is 4 radian

Solution:

Given that,

A circle of radius 1.5 meter that intercepts an arc of length 600 centimeters

To find: Radian measure of the central angle

Let us find the circumference of circle

The circumference of circle is given as:

[tex]\text{ circumference of circle } = 2 \pi r[/tex]

Where "r" is the radius of circle

[tex]\text{ circumference of circle } = 2 \times \pi \times 1.5 = 3 \pi[/tex]

Therefore circumference of circle = [tex]3 \pi[/tex] meters , which subtends central angle of  [tex]2 \pi[/tex] radian

Given that arc of length 600 centimeters. Let us convert 600 centimeter to meter

We know that, to convert centimeter to meter divide the length value by 100

[tex]\text{ 600 centimeter } = \frac{600}{100} \text{ meter } = 6 \text{ meter}[/tex]

Therefore arc of 6 meter will subtend a central angle of:

[tex]\rightarrow \frac{6}{3 \pi} \times 2 \pi = 4[/tex]

Therefore radian measure of the central angle is 4 radian