the sum of x and 25 is less than 75

I will assume that line 4 bisect line x exactly in half. This means that if we solve the last side of the triangle like seen in the pic below we will know what half of line x is

To find the length of the last side of the triangle (let's call this y) you must use Pythagorean theorem

[tex]a^{2} +b^{2}=c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 4

b = y

c = 6

^^^Plug these numbers/variables into the theorem

[tex]4^{2} +y^{2} =6^{2}[/tex]

solve for y

16 + [tex]y^{2}[/tex]  = 36

[tex]y^{2}[/tex] = 20

x = √20

x ≈ 4.472

^^^This is only half of x so if you double it then it will get you the full length of x

4.472 * 2 = 8.944

8.9 (D)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

1, 2 and 3 are interior angles

4 is the exterior angle

The length of the sunken ship is 28.56m

To calculate the length of the sunken ship , we have to calculate the distance between the beneath of the ship to the front and to the back.

distance between the beneath of the ship to back of the sunken ship

Tan 62 = 200/x

x = 200/tan 62

x = 106.34m

distance between the beneath of the ship to front of the sunken ship

Tan 56 = 200/y

y = 200/tan 56

y = 134.90m

The length of the sunken ship = 134 .90 - 106.34

= 28.56m

Answer: -1

Step-by-step explanation:

3x − y − 3z           if x = −2      y = 1     z = −2

Step 1: 3(-2)-1-3(-2)

Step 2: -6-1+6

Step 3: -7+6

Step 4: -1

Answer:

$114.99

Step-by-step explanation:

rt4by5by4by5v4fcefrcekjj3ivc24ino3rmf44g4g

gv5y43t4r3wgy54bt3bt 4hnht6bgrvf

sorry if there is random numbers and letters i am glitchy

Answer:

97.45 • 0.18 = 17.54. 97.45 + 17.54 = 114.99. I think this is right.

Step-by-step explanation:

Answer:

Statements 1, 2, 4, and 5.

Step-by-step explanation:

(Follow along with the diagram)

The first thing we should do is figure out the measure of every angle. We know immediantly that CED is 90 degrees, and consequently CEA is too. This verifies the first two statements. We are told that EB bisects AEC (AEC = CEA).  This means that EB splits AEC into two congruect angles, BEA and CEB. If BEA = CEB, and BEA + CEB = CEA, then BEA and CEB both equal 45 degrees. This verfies statement 4, and helps us start statement 5. Statement 5 says that DEB = 135 degrees. We can see that the angle DEB is made up of angles CEB and CED. We already know that CEB = 45, and CED = 90. 90 + 45 = 135. So, statement 5 is true.

Regarding the incorrect statements, I will explain why they are false. We deduced that BEA = 45, so statement 6, stating that AEB (same as BEA) is 35, is not true. Statement 3 says that CEA = 1/2 of CEB. This equation regards the angles' measurements. If we plug in their known measurements, the equation reads 90 = 1/2 of 45. Through logic, we know this is not true. So, statement 3 is also false.

Statements are true regarding the given statement and diagram1, 2, 4, and 5.

1: ∠CED is a right angle.

2: ∠CEA is a right angle.

3: m∠CEB = m∠BEA

5 : m∠DEB = 135°

The first thing we should do is figure out the measure of every angle. We know immediately that CED is 90 degrees, and consequently, CEA is too. This verifies the first two statements. We are told that EB bisects AEC (AEC = CEA).  

This means that EB splits AEC into two congruent angles, BEA and CEB. If BEA = CEB and BEA + CEB = CEA, then BEA and CEB both equal 45 degrees.

This verifies statement 4 and helps us start statement 5. Statement 5 says that DEB = 135 degrees. We can see that the angle DEB is made up of angles CEB and CED.

We know that CEB = 45, and CED = 90. 90 + 45 = 135. So, statement 5 is true.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.

In general, all congruent angles are not supplementary angles. For angles to add up to 180, they must be supplementary angles. So only right angles are congruent as well as supplementary angles because they have the same measure and they add up to 180.

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Answer:

Yes, they are parallel.

Step-by-step explanation:

Parallel lines have the same slope. We must find the slopes of the two lines.

When the equation of a line is written in the slope-intercept form,

y = mx + b,

the slope is m.

The first line has equation

[tex] y = \dfrac{2}{3}x - 17 [/tex]

It is already written in the slope-intercept form. Comparing y = 2/3x - 17 with y = mx + b, you see that m = 2/3. The slope of the first line is 2/3.

Now we solve the second equation for y to obtain the slope-intercept form of that equation.

4x - 6y = -6

Subtract 4x from both sides.

-6y = -4x - 6

Divide both sides by -6.

[tex] \dfrac{-6}{-6}y = \dfrac{-4}{-6}x + \dfrac{-6}{-6} [/tex]

[tex] y = \dfrac{2}{3}x + 1 [/tex]

We now compare this form of the second equation with y = mx + b, and we see that m = 2/3.

Both equations have the same slope, 2/3, so the lines are parallel.

[tex]\text{Hey there!}[/tex]

[tex]\text{3x}>\text{96}[/tex]

[tex]\text{You have to DIVIDE by 3 on BOTH OF YOUR SIDES.}[/tex]

[tex]\dfrac{3\text{x}}{3}>\dfrac{96}{3}[/tex]

[tex]\text{Cancel out: }\dfrac{3\text{x}}{3}\text{ because it equals to 1}[/tex]

[tex]\text{Keep: }\dfrac{96}{3}\text{ because it helps us solve for our answer, to compare}[/tex] [tex]\text{both numbers.}[/tex]

[tex]\text{96}\div3\text{ = 32}[/tex]

[tex]\boxed{\boxed{\bf{Answer:x > 32}}}\checkmark[/tex]

[tex]\text{It's a}[/tex] [tex]\text{(o)(p)(e)(n)(e)(d) circle shaded to the right side of the number line}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

x>32

Step-by-step explanation:

Divide by 3 from both sides of equation.'

3x/3>96/3

Simplify, to find the answer.

96/3=32

x>32 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer: 5

Step-by-step explanation: The distance between two numbers can be found by finding the absolute value of the difference of the numbers. Put more simply, subtract -3 - 2 to get -5, which has an absolute value of 5. Or, you can do 2 - -3 to get 5, which has the same absolute value of 5.

The distance between -3 and 2 on the number line is 5 units.

It is the measurement done between two points on a surface.

Distance=speed*time

If we plot -3 and 2 on the number we find that -3 will be on the left side of 0 and 2 will be on the right side of 0. To reach 2 from -3 we have to first go to-2 then -1, then 0 and then 0 to 1 and 1 to 2.

Hence we have to go to 5 units. That's why the distance between -3 and 2 is 5 units.

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Answer:

A

Step-by-step explanation:

The equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

Here, the center is (2, 1) and the radius is 1.

(x - 2)² + (y - 1)² = 1²

The equation of the given circle is Option(A)  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

The standard equation of any circle is given as -

[tex](x-h)^{2} + (y - k)^{2} = r^{2}[/tex]  

where (h,k) is the coordinate of the center of the given circle and r is the length of radius of the circle.  

In the diagram given aside, we can see that the circle has its center at (2,1) and also the radius of the circle measures 1 units.

Thus, we have h = 2 , k = 1 and r = 1 in the standard representation.

The equation of the circle is -

⇒ [tex](x-2)^{2} + (y - 1)^{2} = 1^{2}[/tex]

∴  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex]

Therefore, the equation of the given circle is Option (A) [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

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your correct it is 240

lengthxwidthxheight

8x6x5=240

Answer:

1. 0.283333333

2. 0.016666667

3. 0.0833333333333333

4.0.0666666666666667

5. 0.1

6. 0.2

7. 0.05

8.0.0333333333333333

Step-by-step explanation:

Simply divide the numerator by the denominator. ex. 17 divided by 60.

Hope this helps :)

Answer:

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

Step-by-step explanation:

Given equation of line is:

2x-3y=13

We will convert the equation of line in point-slope form to find the slope of the line

Let  

m_1  be the slope of the line

So,

2x-3y=13

-3y= -2x+13

Dividing both sides by -3

(-3y)/(-3)=(-2x)/(-3)+13/(-3)

y=(2/3)x-13/3

The co-efficient of x is the slope of the line.

So,

m_1=2/3

Let

m_2  be the slope of second line

As we know that product of slopes of two perpendicular line is -1

m_1 m_2= -1

2/3*m_2= -1  

m_2= -1*3/2

m_2= -3/2

So m2 is the slope of the line perpendicular to given line.

The standard equation of a line is  

y=mx+b

To find the equation of line through (-6,5), put the point and slope in the given form and solve for b

5= -3/2 (-6)+b

5=18/2+b

5=9+b

b=5-9

b= -4  

Putting the values of slope and b, we get

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

Answer: [tex]y=-\frac{3}{2}x-4[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

To express the given equation of the line in this form, we need to solve for "y":

[tex]2x - 3y = 13\\\\-3y=-2x+13\\\\y=\frac{-2}{-3}x+\frac{13}{-3}\\\\y=\frac{2}{3}x-\frac{13}{3}[/tex]

We can identify that the slope of this line is:

[tex]m=\frac{2}{3}[/tex]

Since the slopes of perpendicular lines are negative reciprocals, then the slope of the other line is:

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

Now, we need to substitute the given point  and the slope into  [tex]y=mx+b[/tex] and solve for "b":

[tex]5=-\frac{3}{2}(-6)+b\\\\5=9+b\\\\5-9=b\\\\b=-4[/tex]

Substituting values, we get that the equation of this line is:

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

Answer:

[tex]\large\boxed{C)\ \left\{\begin{array}{ccc}y=x\\\\y=\dfrac{-x+10}{x-4}\end{array}\right}[/tex]

Step-by-step explanation:

We have the points

(-2 , -2) → x = -2 and y = -2 → x = y

(5, 5) → x = 5 and y = 5 → x = y

The equation of a line is [tex]y=x[/tex]

The hyperbola has the vertical asymptote x = a and the horizontal asymptote y = -1.

Therefore the second equation is:

[tex]y=\dfrac{a}{x-4}-1=\dfrac{a}{x-4}-\dfrac{x-4}{x-4}=\dfrac{a-(x-4)}{x-4}=\dfrac{a-x+4}{x-4}[/tex]

Where a > 0.

The corresponding equation in the solutions to choose is:

[tex]y=\dfrac{-x+10}{x-4}[/tex]

This is a quick sketch of the problem

the answer is about 235.31 ft

you have to use this equation to get the length of the other side, which is roughly 213 ft:

[tex]100 \div \sin(28) [/tex]

then it's just Pythagorean Theorem to get the end result:

[tex] {100}^{2} + {213}^{2} = {c}^{2} [/tex]

To find the distance from the car to the base of the pole, use the tangent function. Plug in the values and solve for the adjacent side.

To find the distance from the car to the base of the pole, we can use trigonometry. Since the observer is looking down at an angle of depression, we can use the tangent function. Tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pole (100 ft) and the adjacent side is the distance from the car to the base of the pole.

So, using the formula tan(angle) = opposite/adjacent, we can plug in the values and solve for the adjacent side:

tan(28 degrees) = 100 ft/adjacent

adjacent = 100 ft / tan(28 degrees)

Using a calculator, we find that the distance from the car to the base of the pole is approximately 169.38 ft.

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Answer:

x = 95 - 4y

Step-by-step explanation:

Let the pieces he has now be a variable x and the no. of students in his class be y, So the pieces he gave to everyone become 4y (note that 4 here means he had given four to each) and as he had won 95 pieces at the fair in the starting,

therefore the equation becomes:-

x = 95 - 4y

The expression for how many pieces of gum Deshawn has now is 95 - (4 x number of students in his math class).

To find out how many pieces of gum Deshawn has after giving four to every student in his math class, we need to subtract the number of pieces of gum he gave away from the total number he won at the county fair.

We can represent this situation using the expression: 95 - (4 x number of students in Deshawn's math class).

For example, if there were 20 students in Deshawn's math class, the expression would be: 95 - (4 x 20) = 95 - 80 = 15.

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Answer:

1. 702 square centimeters

2. m∠YWX = 63°

Step-by-step explanation:

1.

The total surface area is area of all the sides.

Adding all these up  154 + 120 + 120 + 168 + 140 = 702 centimeters square.

2.

Angle WYX is equal to 46° (vertical angles are equal).

Now looking at triangle XWY, we know all three angles will add up to 180°. Given x =71° and Y = 46°, we can figure out W (Angle YWX)

71 + 46 + Angle YWX = 180

Angle YWX = 180 - 71 - 46 = 63°

Second answer choice is correct.

Answer:

F ................................

Answer:

($4.00/x)+($4.50/y)

Step-by-step explanation:

we know that

Apples cost 80 cents for x apples

so

One apple cost $0.80/x

Oranges cost 75 cents for y oranges

so

One orange cost $0.75/y

Find the cost of 5 apples and 6 oranges

Multiply the number of apples by the cost of one apple and multiply the number of oranges by the cost of one orange

so

5($0.80/x)+6($0.75/y)=($4.00/x)+($4.50/y)

Final answer:

The cost of 5 apples at 80 cents each is $4.00 and the cost of 6 oranges at 75 cents each is $4.50. The total cost for 5 apples and 6 oranges is therefore $8.50.

Explanation:

To calculate the cost, in dollars, of 5 apples and 6 oranges at a fruit stand where apples cost 80 cents for x apples and oranges cost 75 cents for y oranges, you can follow these steps:

Determine the cost per apple by dividing 80 cents by x. Since we do not have the value of x, assume x equals 1 for this explanation, making the cost 80 cents per apple.

Multiply the cost per apple by 5 to find the total cost for 5 apples.

Determine the cost per orange by dividing 75 cents by y. Assuming y equals 1 for this explanation, the cost is 75 cents per orange.

Multiply the cost per orange by 6 to find the total cost for 6 oranges.

Add the total cost for apples and oranges to find the combined cost, converting cents to dollars as necessary.

Therefore, the cost for 5 apples is 5 × 0.80 = $4.00, and the cost for 6 oranges is 6 × 0.75 = $4.50. Adding these together, the total cost for 5 apples and 6 oranges is $4.00 + $4.50 = $8.50.

Answer:

2 hours 18 minutes (to the nearest minute)

Step-by-step explanation:

6.5 / 0.5 hours

--> Multiply the whole equation by 4.61538461538 so that 6.5 becomes 30

= 30 papers in 2.30769230769 hours = 02:18:28

Mrs. Bell will take 2 hrs 18 mins approximately.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that 6.5 students' papers can be checked in 0.5 hours

1 student's paper can be checked in 0.5/6.5 hours

30 students' paper can be checked in (0.5 /6.5)*30 hours = 2.307 hours

Therefore, Mrs. Bell will take 2 hrs 18 mins approximately.

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Answer:

Option A is correct.

Step-by-step explanation:

Distance between two points can be calculated from formula

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Here x₁ = 6, y₁ = 2,x₂ = -3 and y₂ = -2

Putting the values in the formula

[tex]d = \sqrt{(-3-(6))^2+(-2-(2))^2}\\d = \sqrt{(-3-6)^2+(-2-2)^2} \\d = \sqrt{(-9)^2+(-4)^2} \\d = \sqrt{81+16}\\d = \sqrt{97}\\d= 9.85[/tex]

So, the distance between points (6, 2) and (-3, -2) is 9.85 or ≈ 9.

So, Option A is correct.

ANSWER

[tex] \sqrt{ 97 }[/tex]

EXPLANATION

The formula for calculating the distance between two points is

[tex]d = \sqrt{ {(x_2-x_1)}^{2} +(y_2-y_1)^{2} } .[/tex]

We use this formula to find the distance between (6,2) and (-3,-2)

We plug in the points to get,

[tex]d = \sqrt{ {( - 3-6)}^{2} +( - 2-2)^{2} } .[/tex]

[tex]d = \sqrt{ {( - 9)}^{2} +( - 4)^{2} } .[/tex]

[tex]d = \sqrt{ 81+16}[/tex]

[tex]d = \sqrt{ 97 }[/tex]

The distance between the two given points is

[tex] \sqrt{ 97 }[/tex]

Answer:

(16,-12)

Step-by-step explanation:

To find where these lines intersect, we must first know their slope. If the slope is equal, then the lines don't intersect and they are parallel.

The best formula for knowing slope is slope-intercept form, y=mx+b whereas m is the slope and b is the y-intercept (where the line crosses x=0)

The first equation is already in slope-intersect form so we can substitute the section that is equal to y into the second equation where y is.

x + 2(-x + 4) = -8

x + -2x + 8 = -8

-x + 8 = -8

-x = - 16

x = 16

Now we can use this known variable to find y.

y = -(16) + 4

y = -16 + 4

y = -12

Answer:

∠QPR must be an acute angle

Step-by-step explanation:

Given : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

To Find :∠QPR must be?

Solution:

Acute Angle : An angle whose measure is less than 90°

Since ∠MPR is an acute angle

This means ∠MPR is less than 90°

Now PQ is in the interior of ∠MPR

So, referring the attached figure

∠QPR should be less than ∠MPR

So, the measure of ∠QPR should be less than ∠MPR

So,  the measure of ∠QPR is also less than 90°

So, ∠QPR must be an acute angle

So, Option D is correct.

Answer: D. Acute

Step-by-step explanation:

We are given that : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

Definition :

Acute Angle : An angle having measure is less than 90°

.

Obtuse angle : An angle having measure is greater than 90° but less than 180

°.

Right angle : An angle whose measure exactly 90°

.

Straight angle : An angle whose measure exactly 180°

.

∵∠MPR is an acute angle  ,

Then ∠MPR must be less than 90°

.

Also, PQ is in the interior of ∠MPR

.

⇒∠QPR should be less than ∠MPR

.

⇒ the measure of ∠QPR is also less than 90°

⇒∠QPR must be an acute angle  . [By definition of Acute angle.]

Hence, the correct answer is option D.

Answer:

D

Step-by-step explanation:

f(2)=4(2)-12

=8-12

=-4

Answer:

D. -4

Step-by-step explanation:

We have the following function:

[tex]f(x)=4x-12[/tex]

and we are asked to find the value of the function [tex]f(x)[/tex] when the variable [tex]x[/tex] is equal to 2:  [tex]f(2)[/tex].

This means that we must substitute the value of [tex]x = 2[/tex] wherever there is an [tex]x[/tex] in the function:

[tex]f(2)=4(2)-12[/tex]

[tex]f(2)=8-12[/tex]

[tex]f(2)=-4[/tex]

The answer is D. -4

Answer:

Distributive Property.

Step-by-step explanation:

Cos(A-B)= Cos A- Cos B

The variables in the parenthesis gets multiplied into the Cos

Cos A - Cos B

Answer:

2:30 pm

Step-by-step explanation:

In two hours (from 10am), she is 45 * 2 = 90 miles from vacation cabin.

From then on her average is still 45 mph and her husband's is 65 mph. So, husband catches her 20 miles (65-45=20) in every hour.

The husband has to catch up 90 miles. How long would it take if he is catching up at 20 miles an hour?

90/20 = 4.5 hours

So husband starts at 10am and 4.5 hours form that time is 2.30pm

The correct answer is (D) 1,155 miles (rounded to the nearest whole number).

To find the round trip distance from Kansas City to Denver, we need to calculate the actual distance in miles based on the scale given in the map.

On the map, 1 inch represents 3 miles. The distance from Kansas City to Denver on the map is given as 192 inches. To find the actual distance in miles:

Actual distance = (Distance on the map) × (Scale factor)

Actual distance = 192 inches × 3 miles/inch

Actual distance = 576 miles

Since the round trip distance includes going from Kansas City to Denver and back, we need to double the actual distance:

Round trip distance = 2 × 576 miles

Round trip distance = 1152 miles

So, the correct answer is (D) 1,155 miles (rounded to the nearest whole number).

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Answer:

0 Siblings: 4 Students

3 or more siblings: 5 students

Step-by-step explanation:

The numbers at the bottom represents how many siblings they have and the dots represent the number of studens so using this we know:

0 Siblings: 4 Students

1 Sibling: 3 Students

2 Siblings: 3 Students

3 Siblings: 1 Student

4 Siblings: 0 Students

5 Siblings: 2 Students

6 Siblings: 1 Student

7 Siblings: 1 Student

3 or more: 1 + 0 + 2 + 1 + 1 = 5

3 or more siblings: 5 students

Answer:

0 Siblings: 4 Students3 or more siblings: 5 students

Step-by-step explanation:

Answer:

The correct answer is B. point

Step-by-step explanation:

We know that a line has a length so option a cannot be correct.

A point is represented by a dot which has no length, width and height.

A ray is formed by a collection of points which altogether make its length.

Similarly an angle is formed by two rays.

So, angle, ray and line, all of them have length, width or height.

Hence, B. Point is the right answer ..

Answer:

40%

Step-by-step explanation:

2 out of 5 of the rectangles are shaded. With a ratio of 2/5 this represented as a percent is 40%

Answer:

40%.

Step-by-step explanation:

2 out of 5 rectangles are shaded.

As a percentage that is 2/5 * 100 = 40%.