7. The coordinates of the vertices of a rectangle are go
I by
R(-3,-4), E(3, 4), C(4,4), and T(4-4). Plot these points
on the coordinate plane at the right and connect them to
draw the rectangle. Then connect points E and T to form
diagonal ET.
a. Use the Pythagorean Theorem to find the exact
length of ET.
b. How can you use the Distance Formula to find the
length of ET? Show that the Distance Formula gives
the same answer
​

Answer:

11

Step-by-step explanation:

We are given the following expression which we are to solve:

[tex] - 2 9 + 4 0 [/tex]

Since there are no brackets, multiplication or division signs so we will solve this from left to right starting from the negative sign.

Adding 40 to -29 or subtracting 29 from 40 is the same so we get:

[tex] - 2 9 + 4 0 = 1 1 [/tex]

Answer:

V = s^3

V = 729 ft^3 when the side length is 9 ft

Step-by-step explanation:

The volume of a cube is given by

V = s^3  where s is the length of a side

Assuming you mean the side length is 9 ft

V = 9^3

V = 9*9*9

V =729 ft^3

Answer:

x = 8

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other two sides, thus

x² + 6² = 10²

x² + 36 = 100 ( subtract 36 from both sides )

x² = 64 ( take the square root of both sides )

x = [tex]\sqrt{64}[/tex] = 8

Answer:

z = 24°

Step-by-step explanation:

The 3 angles 48, x and x form a straight angle and sum to 180°, thus

x + x + 48 = 180

2x + 48 = 180 ( subtract 48 from both sides )

2x = 132 ( divide both sides by 2 )

x = 66

The 3 angles in a triangle sum to 180°

sum the 2 known angles and subtract from 180

z = 180° - (66 + 90)° = 180° - 156° = 24°

Answer:

z=24

Step-by-step explanation:

Step-by-step explanation:

hope it helps you!!!!!!!!!!

Answer: x=11.67

Step 1

Use the following equation to find x. We can use this equation because Triangle 1 (triangle within triangle ABC) and Triangle 2 (triangle ABC) are proportional and we can use the system of equations below to create and equation.

[tex]\frac{x}{9}=\frac{x+5}{12}[/tex]

Step 2

We can then use the equation below by cross multiplying the previous equation in step 1.

12x= 9x+35

Step 3

Then solve the equation to find x!

12x=9x+35

3x=35

x=11.67 (rounded to the nearest hundredth)

Answer:

20.922

Step-by-step explanation:

Evaluate ln 7.2 on a calculator; the correct result is 1.974.

Multiply that by 3, obtaining 5.922.

Finally, add 15 to that result:  y = 15 + 3 In 7.2 = 20.922

Answer

-4-(-10)

explain

-4+10=6

the dude above me is correct

Answer:

It is angle 4 because they make 90 degrees together. This is if there are choices for the problem.

It would be ∠4

Angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

From the angle diagram, angle 4 makes the complete right angle.

The sum of the complementary angles is 90 degree

Angle 3 + Angle 4 = 90 degree

Thus, angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.

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I hope to understood my writing

To determine at what time the two lorries will meet, we can use the concept of relative speed. Since the lorries are moving towards each other, their relative speed is the sum of their individual speeds.
The speed of the first lorry is 63 km/h and the speed of the second lorry is 67 km/h. Together their combined speed is:
63 km/h + 67 km/h = 130 km/h
Now we need to calculate how long it will take for them to cover the distance of 520 km between the two towns at their combined speed.
The time taken to cover a distance is equal to the distance divided by the speed, so the time taken \( t \) in hours can be found by:
\( t = \frac{distance}{speed} \)
Substituting the known values into this formula gives us:
\( t = \frac{520 km}{130 km/h} = 4 \) hours
Now we know the lorries will meet after 4 hours of travel.
Given that the lorries start to travel at 7:30 am, we add 4 hours to that time to find the meeting time.
7:30 am + 4 hours = 11:30 am
Therefore, the two lorries will meet at 11:30 am.

Answer:

Measure B= 121

Measure C=59

Step-by-step explanation:

10x-19=7x+23

3x=42

x=14

plug in x to the problem and you'll find Measure B is 121 so to find Measure C you'll have to subtract 180 and 121 to get 59.

The value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B

It is defined as the four-sided polygon in geometry having four edges and four corners and two pairs of congruent sides. It has one pair of opposite congruent angles.

We have a quadrilateral in which angle B and angle D are given.

As we know the opposite angles in the quadrilateral are same in measure.

10x - 19 = 7x + 23

3x = 42

x = 14

Angle B =  10x - 19 = 10(14) - 19 = 121 degree

Angle C =  7x + 23 = 7(14) + 23 = 121 degree

Angle A + Angle C = 360 - 121 -121 = 118

Angle C = 118/2 = 59

Thus, the value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B

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Answer:

279 ft^2

Step-by-step explanation:

The area of a rectangle of length L and width W is A = LW.

Here, that area is (19.25 ft)(14.5 ft) = 279.125 ft^2, or approx. 279 ft^2

Answer:

the answer would be 3.25 meters

Answer:

3 meters and 25 centimeters of ribbon

Step-by-step explanation:

Answer:

w=4

Step-by-step explanation:

adding a negative is like subtracting so w=11-7

Answer:

w = 4

Step-by-step explanation:

w = 11 + (-7)

w = 11 - 7

w = 4

Answer:

A' will be located 10 units from point A along ray PA

Step-by-step explanation:

we know that

The scale factor is equal to 3

To obtain PA', multiply PA by the scale factor

so

PA'=PA*3

PA=5 units

substitute

PA'=(5)*3=15 units

AA'=PA'-PA=15-5=10 units

therefore

A' will be located 10 units from point A along ray PA

Answer:10 units

Step-by-step explanation:

Answer:

3,4,5 are congruent angles

Step-by-step explanation:

Congruent Angles have the same angle (in degrees or radians). That is all. They don't have to point in the same direction. They don't have to be on similar sized lines.

Answer:

#3 is congruent by SAS; #4 is congruent by SSS; #5 is congruent by AAS; #6 is congruent by ASA

Step-by-step explanation:

For #3, there are sides marked in each so we know we have 2 congruent sides, but the angle where the triangles meet are vertical angles.  So that congruency statement is SAS

For #4, there are again two sides marked in each triangle giving us 2 congruent sides, but since the two triangles share that one side, that gives us the third side for SSS

For #5, we have two angles marked congruent between the two triangles and they also share a side, so AAS is the congruency statement for that one

For #6, again 2 congruent angles and a shared side between, so ASA on that one.

You're in geometry now, yes?

Answer:

444

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x^2+11=36\qquad\text{subtract 11 from both sides}\\\\x^2=25\to x=\pm\sqrt{25}\\\\x=-5\ or\ x=5\\============================\\\\\dfrac{x^2-25}{x+5}=0\qquad Domain:\ x+5\neq0\to x\neq-5\\\\\dfrac{x^2-25}{x+5}=0\to x^2-25=0\qquad\text{add 25 to both sides}\\\\x^2=25\to x=-5\notin D\ or\ x=5\in D[/tex]

The solution is :the ages of the three are: 12, 15, 6.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

1)

Let x - Kareem's age => Sadie's age - x + 3, Nadra - x/2

We end up with the expression;

x + x + 3 + x/2 = 33

Multiply by 2 to get rid of the fraction;

2x + 2x + 6 + x = 66

5x = 60

x = 12 - Kareem's age;

2) x + 3 = 12 + 3 = 15 - Sadie's age;

3) x / 2 = 12 / 2 = 6 - Nadra's age;

Hence, The solution is :the ages of the three are: 12, 15, 6.

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Final answer:

The student's first error in determining the ages of Sadie, Kareem, and Nadra was in the setup of the equation, incorrectly representing Nadra's age as 2x instead of ½x. Correcting this mistake involves modifying the equation to accurately reflect the relationships between their ages.

Explanation:

The first error made by the student is in the setup of the initial equation for the ages of Sadie, Kareem, and Nadra. The equation (x + 3) + x + 2x = 33 inaccurately represents Nadra's age in relation to Kareem's. Given that Kareem is twice as old as Nadra, Nadra's age should be represented as ½x (half of Kareem's age), not 2x.

Correcting the initial equation should look like this: (x + 3) + x + ½x = 33. This equation accurately represents Sadie being 3 years older than Kareem and Kareem being twice as old as Nadra. To solve this corrected equation, we first combine like terms to simplify: 2½x + 3 = 33. Then, we solve for x to determine each person's age correctly.

Answer: Option E

[tex]0.120\ g[/tex]

Step-by-step explanation:

The exponential decay formula is:

[tex]C (t) = pe^ {-rt}[/tex]

Where p is the initial amount of Ytterbium

r is the rate of decrease

C(t) is the amount of Ytterbium in grams as a function of time

t is the time in days

In this problem:

[tex]p = 80\ g\\\\r=\frac{50\%}{100\%}\\\\r=0.5[/tex]

t is the time in units of 4.2 days

Then

[tex]C(t) = 80e^{-0.5t}[/tex]

We want to calculate the amount of Ytterbium in 54.6 days.

Then as t is the time in units of 4.2 days

[tex]t = \frac{54.6}{4.2} = 13\\\\t = 13[/tex]

Finally

[tex]C(t=13) = 80e^{-0.5*13}[/tex]

[tex]C(t) = 0.120\ g[/tex]

2x ≤ 30

You must isolate x. To do this divide 2 to both sides

2x/2 ≤ 30/2

x ≤ 15

x is less then or equal to 15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: x ≤ 15

Step-by-step explanation:

Because...

2x ≤ 30

[tex]\frac{2x}{2} \leq \frac{30}{2}[/tex]

so after dividing 30 by 2 you get 15.

* Therefor, the answer is x ≤ 15

* Hopefully this helps:) Mark me the brainliest:)!!!

See the attached picture:

Answer:

-4

Step-by-step explanation:

(1/4)*x-(1/8) = (1/2)*x+7/8

First rearrange the numbers

(1/4)*x-((1/2)*x)-(1/8)-(7/8)

1/4*x ((-1/2)*x)-(1/8)-(7/8)

-1/4*x-1 = 0 + 1

-1/4*x = 1  -1/4

x = 1/(-1/4)

x = -4

x = -4

For this case we must find an expression equivalent to:

[tex]log_ {5} (\frac {x} {4}) ^ 2[/tex]

So:

We expanded [tex]log_ {5} ((\frac {x} {4}) ^ 2)[/tex]by moving 2 out of the logarithm:

[tex]2log_ {5} (\frac {x} {4})[/tex]

By definition of logarithm properties we have to:

The logarithm of a product is equal to the sum of the logarithms of each factor:

[tex]log (xy) = log (x) + log (y)[/tex]

The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.

[tex]log (\frac {x} {y}) = log (x) -log (y)[/tex]

Then, rewriting the expression:

[tex]2 (log_ {5} (x) -log_ {5} (4))[/tex]

We apply distributive property:

[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]

Answer:

An equivalent expression is:

[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]

Answer: the answer is c

Step-by-step explanation: 2log5x-2log54

By moving the decimal according to the number of places expressed by the exponents, we can see the real value of each answer choice.

A. .0008 lbs not a realistic weight for an 18-wheeler

B. 800 lbs closer but still not enough weight

C. .08 nope not this one either.

D. 80,000 lbs. this is probably in the range we are looking for.

If the exponent is negative, move the decimal that many spaces left. If the exponent is positive, move the decimal that many space right.

The correct answer is D.

Answer:

The reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]

Step-by-step explanation:

The average and legally maximum weight of an 18-wheeler is 80,000 pounds.

From option a through d, we check which of the measurement is close or equivalent to 80,000 pounds

By converting this, we have

[tex]= 8 * \frac{1}{10000} lb[/tex]

[tex]= \frac{8}{10000} lb[/tex]

[tex]= 0.0008 lb[/tex]

By converting this, we have

[tex]= 8 * 100 lb[/tex]

[tex]= 800 lb[/tex]

By converting this, we have

[tex]= 8 * \frac{1}{100} lb[/tex]

[tex]= \frac{8}{100} lb[/tex]

[tex]= 0.08 lb[/tex]

By converting this, we have

[tex]= 8 * {10000} lb[/tex]

[tex]= {80000} lb[/tex]

From the 4 conversions, only  [tex]8 * 10^{4} lb[/tex] is equivalent to the average and legally maximum weight of an 18-wheeler, 80,000 pounds.

Hence, the reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]

Oops wrong one man I’m sorry

Answer: The function would be,

[tex]P(x)=50000(1.04)^x+35000(1.055)^x[/tex]

The approximate total profit after 4 years is $ 97341.65.

Step-by-step explanation:

Given,

For branch A,

First year profit = $ 50,000,

And, the profit increased by 4% every year.

Thus, the profit of branch A after x years,

[tex]P_1=50000(1+\frac{4}{100})^x[/tex]

[tex]\implies P_1=50000(1.04)^x[/tex]

Also, for branch B,

First year profit = $ 35,000,

And, the profit increased by 5.5% every year.

Thus, the profit of branch B after x years,

[tex]P_2=35000(1+\frac{5.5}{100})^x[/tex]

[tex]\implies P_2=35000(1.055)^x[/tex]

Hence, the total profit,

[tex]P=P_1+P_2[/tex]

[tex]\implies P(x)=50000(1.04)^x+35000(1.055)^x[/tex]

Which is the required function.

After 4 years, x = 3,

Therefore, the total profit after 4 years would be,

[tex]\implies P(3)=50000(1.04)^3+35000(1.055)^3=\$ 97341.648125\approx \$ 97341.65[/tex]

Answer: The number is 8

Step-by-step explanation:

 Let be "x" the certain number. Then "3 times a certain number" means that the number "x" is multiplied by 3. This is:

[tex](3)(x)=3x[/tex]

Now, "3 times a certain number is increased by 4" means that the we must add 4 to [tex]3x[/tex], in other words, this indicate an addition:

 [tex]3x+4[/tex]

And finally "3 times a certain number is increased by 4 the result is 28" means that  [tex]3x+4[/tex] is equal to 28. Then the expression is:

 [tex]3x+4=28[/tex]

To find the number "x", subtract 4 from both sides of the equation:

[tex]3x+4-4=28-4[/tex]

[tex]3x=24[/tex]

Dividing both sides of the equation by 3, you get that the number is:

[tex]\frac{3x}{3}=\frac{24}{3}\\\\x=8[/tex]

Answer:

$17,930.12

Step-by-step explanation:

A suitable financial calculator can tell you the unpaid balance is $17,930.12 after 60 monthly payments of $149.

___

It seems likely the formulas and examples in your reference material will be helpful, too.

Answer: $17,930.12

Step-by-step explanation:

confirmed

Multiply the bracket by 3

3(2f+g+4)

My answer is 6f+3g+12

Answer is true

This is true. You applied the Distributive Property authentically.

Final answer:

0.64 is a finite decimal with zero repeating digits as it does not have digits that continue infinitely after the decimal.

Explanation:

The number 0.64 is a decimal that has two digits after the decimal point. These digits (6 and 4) do not repeat infinitely, making them non-repeating decimal digits. Therefore, there are zero repeating digits in 0.64. A repeating decimal would have one or more digits after the decimal point that continue infinitely, often denoted by a bar over the repeating digits. Since 0.64 does not exhibit this pattern, it is a finite decimal.