Which of the following is a true proportion of the figure based on the triangle proportionality theorem? Question 13 options: A) ab=ba B) cd=ab C) db=ac D) cb=ab

Answer:

15.62 = x

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

10 ^2 + 12^2 = x^2

100 +144 = x^2

244 = x^2

Take the square root of each side

sqrt(244) = sqrt(x^2)

15.62049935 = x

Rounding to the nearest hundredth

15.62 = x

Answer:

15.62

Step-by-step explanation:

We can use the Pythagorean Theorem.

10^2+12^2=c^2

100+144=c^2

244=c^2

15.62=c, or x=15.62

The correct option is A. The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is: y - 9 = 1/2(x + 3).

To find the equation of a line perpendicular to y = -2x + 8 that passes through the point (-3, 9), we need to determine the slope of the perpendicular line.

The given equation is in slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope of the given line is -2.

Since the perpendicular line has a slope that is the negative reciprocal of -2, we can determine its slope as 1/2.

Now that we have the slope (1/2) and a point (-3, 9) on the line, we can use the point-slope form of a line to write the equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

Plugging in the values, we get:

y - 9 = 1/2(x - (-3))

Simplifying:

y - 9 = 1/2(x + 3)

Rearranging to match the given options:

y - 9 = 1/2(x) + 3/2

The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is:

y - 9 = 1/2(x + 3)

Therefore, the correct option is A.

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Complete question is below

Identify an equation in point-slope form for the line perpendicular to

y=-2x+ 8 that passes through (-3,9).

A. y - 9 = 1/2(x+3)

B. y+3 = 3(x-9)

C. y - 9 = (x + 2)

D. y + 9 = 1/2(x – 3)

Answer:

ab² - a²b

Step-by-step explanation:

a²b⁴ - b²a⁴ can be factored as a²b²(b² - a²) which becomes a²b²(b + a)(b - a). Since the numerator and denominator both have (a + b) and ab the final answer is ab(b - a) = ab² - a²b.

Answer:

1)

[tex]\text{ Slope = -3}[/tex]

2)

[tex]y+4=-\frac{7}{8}(x-7)[/tex]

3)

[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]

Step-by-step explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

1)

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

[tex]m=\frac{3-(-4)}{-1-7}[/tex]

Subtract. So, our slope is:

[tex]m=\frac{7}{-8}=-7/8[/tex]

2)

Now, let's use the point-slope form:

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

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

[tex]y-(-4)=-\frac{7}{8}(x-7)[/tex]

Simplify. So, our point-slope equation is:

[tex]y+4=-\frac{7}{8}(x-7)[/tex]

3)

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

[tex]y+4=-\frac{7}{8}x+\frac{49}{8}[/tex]

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

[tex]y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}[/tex]

Subtract. So, our slope-intercept equation is:

[tex]y=-\frac{7}{8}x+\frac{17}{8}[/tex]

And we're done!

Answer: Shown Below

Step-by-step explanation:

1. -7/8

2. y+4= (-7/8)(x-7)

3. y=(-7/8)x+ (17/8)

Just did it

Answer:

A. 85

Step-by-step explanation:

SInce nickels are worth 5 cents, the number of pennies must end with an 8 or a 3 in order for the total to end with a 3 ($9.83)

Answer:

Whenever  [tex]a\leq 5[/tex].

Step-by-step explanation:

We can play around with some numbers and develop some rules for this equation.

Note that the number 5 and -5 are used here, so let's try using 5 as a.

[tex]|5-5| = 5-5\\|0| = 0\\0 = 0[/tex]

So 5 works. Let's try a random number like 3.

[tex]|3-5| = 5-3\\|-2| = 2\\2 = 2[/tex]

Okay, with this info we know that we might be able to develop one rule that [tex]a<5[/tex]. Just to test, let's try 0, -3, and -5.

[tex]|0-5| = 5-0\\|-5| = 5\\5 = 5[/tex]

Zero works.

[tex]|-3 - 5| = 5-(-3)\\|-8| = 8\\8 = 8[/tex]

-3 works.

[tex]|-5 -5| = 5-(-5)\\|-10| = 10\\10 = 10[/tex]

-5 works. Now, this might stop here making the equation [tex]-5 \geq a \leq 5[/tex], so let's test a number outside of -5 - say -20.

[tex]|-20 - 5| = 5-(-20)\\|-25| = 25\\25 = 25[/tex]

Yes! This works, so a works for this equation as long as [tex]a \leq 5[/tex].

Hope this helped!

Answer:

A =200.96 ft^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

The radius is 8

A = pi 8^2

A = 64 pi

Letting pi = 3.14

A = 64 ( 3.14)

A =200.96 ft^2

Answer:

[tex]\boxed{\mathrm{200.96 \: feet^2}}[/tex]

Step-by-step explanation:

Apply formula for the area of a circle.

[tex]area=\pi r^2[/tex]

The radius is 8 ft.

[tex]A=\pi (8)^2[/tex]

[tex]A=64\pi[/tex]

Take [tex]\pi[/tex] as 3.14

[tex]A=64(3.14)[/tex]

[tex]A=200.96[/tex]

Answer:

x ≤ -1

Step-by-step explanation:

The domain is the x-values.  Since the graph shows all numbers up to -1, the domain would be all numbers less than or equal to -1:

x ≤ -1

Answer:

The temperature order are;

(b) 96.62 K = (d) 96.62 K > (a) 48.31 K = (c) 48.31 K = (e) 48.31 K =  (f) 48.31 K

Arrangement in order from highest to lowest and alphabetically gives;

(b) ↔ (d) → (a)↔ (c)↔ (e)↔ (f)

Step-by-step explanation:

From the universal gas equation

P×V = N×k×T

Where:

P = Pressure

V = Volume

N = Number of molecules

k = Boltzmann constant = 1.38 × 10⁻²³ J/K

T = temperature

Therefore;

[tex]T =\dfrac{P \times V}{k \times N}[/tex]

Which gives;

(a) When P = 100 kPa = 100,000 Pa, V = 4 L = 0.004 m³, N = 6 × 10²³, we have

100000*0.004/(6*10^(23)*1.38*10^(-23)) = 48.31 K

(b) When P = 200 kPa = 200,000 Pa, V = 4 L = 0.004 m³, N = 6 × 10²³, we have

200000*0.004/(6*10^(23)*1.38*10^(-23)) = 96.62 K

(c) When P = 50 kPa = 50,000 Pa, V = 8 L = 0.008 m³, N = 6 × 10²³, we have

50000*0.008/(6*10^(23)*1.38*10^(-23)) = 48.31 K

(d) When P = 100 kPa = 100,000 Pa, V = 4 L = 0.004 m³, N = 3 × 10²³, we have

100000*0.004/(3*10^(23)*1.38*10^(-23)) = 96.62 K

(e) When P = 100 kPa = 100,000 Pa, V = 2 L = 0.002 m³, N = 3 × 10²³, we have

100000*0.002/(3*10^(23)*1.38*10^(-23)) = 48.31 K

(f) When P = 50 kPa = 50,000 Pa, V = 4 L = 0.004 m³, N = 3 × 10²³, we have

50000*0.004/(3*10^(23)*1.38*10^(-23)) = 48.31 K

Answer:

Step-by-step explanation:

2 + 3² * ( 3 -1) = 2 + 9 * 2

                     = 2 + 18

                     = 20

Answer:

20

Step-by-step explanation:

2 + 3² · (3 - 1)

= 2 + 3² · 2 -- (3 - 1 = 2)

= 2 + 9 · 2 -- (3² = 9)

= 2 + 18 -- (2 · 9 = 18)

= 20

Answer:

A, B, C

Step-by-step explanation:

4 - (-5) + 0

4 - (-5) = 4 + 5 (because a negative + negative = positive)

4 + 5 = 9

a, b and c all equal 9

hopefully this helped you!! :3

Answer:

1) A bar diagram with 2 shaded squares and 8 unshaded squares.

Step-by-step explanation:

There are 100 students (40+15+20+25).

20 signed up for Track and Field.

20 out of 100 would equate to 20/100, or 2/10, or:

1) A bar diagram with 2 shaded squares and 8 unshaded squares.

Answer:

a

Step-by-step explanation:

the two squares are shaded and eight are not

Answer:

Option A.

Step-by-step explanation:

there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents.

Let x and y be the number of stamps of 40 cents and 55 cents respectively.

Total number of stamps is 45. So

[tex]x+y=45[/tex]

Total cost of stamps is $18.75. So

[tex]0.40x+0.55y=18.75[/tex]

But Krista wrote the system of equations as

[tex]0.40x+y=45[/tex]

[tex]x+0.55y=18.75[/tex]

Krista put 0.40 in the first equation meant for the number of stamps.

Krista did not write 0.40 in the second equation meant for the value of stamps.

Therefore, the correct option is A.

Answer:

The answer is A

Step-by-step explanation:

TOOK THE TEST!

Answer:

2/9

Step-by-step explanation:

We want  blue green in any order.  That means BG  or GB

There are 9 possibilities

P ( BG or GB ) = number of BG or GB's / total

                       = 2/9

Answer:

48 degrees for A and 7 12 degrees for B

Step-by-step explanation:

As you can see in the first picture, C and x share the same angle and the angle is 48 degrees. On the second picture the answer is 12 because 3*4=12.

Answer:

1/2 (or) 0.50 (or) 50%

Step-by-step explanation:

10 out of 20 wedges are worth more than 10.

10/20 = 1/2 (or) 0.50 (or) 50%

Answer:

0.75

Step-by-step explanation:

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

[tex]\angle AED = \angel BEC[/tex] ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

[tex]\angle ABC = 90^{\circ}[/tex]

In ΔDBC

BC=DC (Given)

So,[tex]\angle CDB=\angle DBC[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle CDB=\angle DBC=x[/tex]

So,[tex]\angle CDB+\angle DBC+\angle BCD = 180^{\circ}[/tex] (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So,[tex]\angle CDB=\angle DBC=x = 65^{\circ}[/tex]

Now,

[tex]\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90[/tex]

So,[tex]\angle ABD=90-x=90-65=25^{\circ}[/tex]

In ΔABD

AB = BD (Given)

So,[tex]\angle BAD=\angle BDA[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle BAD=\angle BDA=y[/tex]

So,[tex]\angle BAD+\angle BDA+\angle ABD = 180^{\circ}[/tex](Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively

Answer:

D) 2.0

Step-by-step explanation:

We know that √2 = 1.414213562 ≈ 1.4, π ≈ 3.14, and √5 = 2.236067978 ≈ 2.2 . Next, I found out that √2π = 4.442882938 which rounds to 4.4. Then, I found out that 4.4 ÷ √5 equals to 1.96773982. So, if we round our answer to the nearest whole number, we will get 2.

Answer:

[tex]\boxed{Option \ D}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{2} \pi }{\sqrt{5} }[/tex]

Where [tex]\sqrt{2}[/tex] = 1.4 , π = 3.14 and [tex]\sqrt{5}[/tex] = 2.24

Plugging in the values

=> [tex]\frac{(1.4)(3.14)}{2.24}[/tex]

=> 4.396/2.24

=> 1.9

≈ 2.0

Answer:

y=|x+1|

Step-by-step explanation:

The y value appears to be 1 more than the x value, so we need to add one to the x to make them even. (x+1)

But the y value doesn’t go below zero, so we need to add the absolute value brackets |x+1|

So y=|x+1|

The graph represents the equation : g(x) = |x + 1|

We have a graph given to us.

We have to write the algebraic expression depicting this graph.

The modulus of the function y = f(x) = x is given by -  

y = |x| = [tex]\left \{ {{x\;\;for\;x > 0} \atop {-x\;\;for\;x < 0}} \right.[/tex]

Using the above property, we can find out the number of solutions of any modulus equation.

The algebraic equation for the graph can be written as -

g(x) = [tex]\left \{ {{x+1;\;for\;x \geq 0} \atop {-x-1\;for\;x < 0}} \right.[/tex]

In the form of modulus function, we can write the above equation as -

g(x) = |x + 1|

Hence, the graph represents the equation : g(x) = |x + 1|

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Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.

The area of the figure decreases when the dimension is decreased

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the figure be represented as ABCD

where ABCD is a rectangle

Now , the measures of the sides of the rectangle be

The length of the rectangle = L

The width of the rectangle = W

And , Area of Rectangle = Length x Width

On simplifying , we get

Area of rectangle = LW

when the dimension of one of the unit is decreased , we get

when L = L/2

Area of rectangle = ( LW) / 2

So , the area of the figure is decreased bu ( 1/2 )

Hence , the area of the figure decreases

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Answer:

(-6,6), (0,12), (4,8)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 2 --> 2(x, y)

Before-> After dilation

2(-3,3) = (-6,6)

2(0,6) = (0,12)

2(2,4) = (4,8)

Please leave a 'thanks' if this helps!

Answer:

Marilyn likes classical

Donna and Valr likes either pop or hiphop

Answer

30 minutes

Step-by-step explanation:

Answer: approximately 26.66667  minutes

This converts to 26 minutes, 40 seconds

=================================================

Explanation:

Let's say there are 360 newspapers that need to be delivered.

The two brothers can get the job done in 40 minutes if they work together. Their rate is 360/40 = 9 newspapers per minute.

Richie can do the full job alone in 90 minutes. So his rate would be 360/90 = 4 newspapers per minute. In 30 minutes, he delivers 30*4 = 120 newspapers. This leaves 360 - 120 = 240 left over.

Divide this over the rate of 9 papers per minute to get 240/9 = 26.66667 approximately. It takes about 26.66667 minutes to finish up delivering the 240 remaining newspapers if the brothers work together.

The portion 0.66667 multiplies with 60 to get 0.66667*60 = 40.0002 which rounds to 40 (we have rounding error going on). This means

26.66667 minutes = 26 minutes, 40 seconds

Answer:

its not a right triangle

Step-by-step explanation:

Answer:

8 times a number plus 7

Step-by-step explanation:

if helps please mark brainliest!! Thanks!

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is D.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression 8t+7 can be best described as 8 times a number plus 7.

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Answer:

[tex]x=\frac{7}{8}[/tex]

Step-by-step explanation:

[tex]10x-3-2x=4[/tex]

First, collect and rearrange the like terms.

[tex]10x-3-2x=4[/tex]

[tex]8x-3=4[/tex]

[tex]8x=4+3[/tex]

Then, solve the equation:

[tex]8x=4+3[/tex]

[tex]8x=7[/tex]

[tex]x=\frac{7}{8}[/tex]

So, the answer is [tex]x=\frac{7}{8}[/tex]. Hope my solution and explanation can help you. Thank you!

If you still cannot get the point, you can ask me anytime.

Answer:

x=7/8

Step-by-step explanation:

10x-3-2x=4

collect like term

8x-3=4

move constant to the right-hand side and change its sign

8x-3=4 into 8x=4+3

add up the number : 8x=4+3

8x=7 divide both sides of the equation by 8

x = 7/8

Answer:

-10a4 + 17d4s2 - 6s2

Step-by-step explanation:

On Edgenuity

Answer:

y ≤ (1/2)x + 2

Step-by-step explanation:

Find the equation of the solid line.  It is immediately evident that the y-intercept is (0, 2).  The line also passes through (-4, 0).  Starting at (-4, 0), x (the run) increases by 4 to 0 and y (the rise) increases from 0 to 2.  Thus, the slope of this line is m = rise / run = 2/4, or m = 1/2.

Thus the equation of the line is y ≤ (1/2)x + 2.

Answer:

No more than ≥

Not under ≤

No less than ≤

maximum ≥

Greater than or equal to ≥

Less than or equal to ≤

Does not exceed ≥

At most ≥

At least ≤

Minimum ≤