Answer:
2x + 12
Step-by-step explanation:
Use the distributive property of multiplication over addition.
2(x + 6) = 2 × x + 2 × 6 = 2x + 12
A cell phone tower covers a circular area with a radius of 15 miles.
(a) If the tower is located at the origin, write an equation for this circular area of coverage.
If the tower is located at the origin, the equation of its circular area of coverage is [tex]x^{2} +y^{2} = 225[/tex]
A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.
The equation of a circle with center at (h, k) and radius r is given by:
[tex](x - h)^{2} + (y-k)^{2} = r^{2}[/tex]
According to the given condition,
center is origin i.e., (h, k) is (0,0)
and r = 15.
Substituting these values in the equation above,
[tex](x - 0)^{2} + (y-0)^{2} = 15^{2}[/tex]
[tex]x^{2} + y^{2} = 225[/tex]
Thus, the equation of the tower located at origin and having coverage area of radius 15 miles is [tex]x^{2} + y^{2} = 225[/tex].
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Ten students sit a test consisting of 20 questions. Two students get 8 questions correct and one student gets 9 questions correct. The remaining seven students all get at least 10 questions correct and the average number of questions answered correctly by these seven students is an integer. If the average number of questions answered correctly by all ten students is also an integer, then that integer is
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Answer:
14
Step-by-step explanation:
That equation, with the given constraints, is easily solved using logical reasoning.10y is a multiple of 5, and 25 is a multiple of 5; that means 7x is a multiple of 5.And we know x is a number between 10 and 20. So x has to be 14
Find the coordinates of the midpoint of a segment with the given endpoints. A(13,14), C(3,5)
The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(13, 14) and C(3, 5).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(13 + 3) / 2, (14 + 5) / 2]
(x, y) = (16/2, 19/2)
(x, y) = (8, 9.5)
The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).
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Collaborate
CSP Use Math Tools Work with a partner. If the measure of 21 in
the figure at the right is 40°, determine the measure of each given
angle without using a protractor. Then check your answers by
measuring with a protractor.
1. 22
3. 24
5. 26
7. 28
2. 23
4. 25
BeacO0CCO
6. 27
>
The measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.
What is an angle?The angle is the separation of the crossing surfaces or lines. Additionally, the angle is specified in degrees. One whole spin has an arc of 360 degrees.
If the total of two angles is 180 degrees, they are said to be supplementary angles.
In the third line, if two lines are parallel. Equal angles are formed by matching angles.
When two lines intersect, then their opposite angles are equal.
The measure of angle ∠1 is 40°.
Angle ∠1 and angle ∠2 are supplementary angles. Then the measure of angle ∠2 will be
∠1 + ∠2 = 180°
40° + ∠2 = 180°
∠2 = 140°
The vertical angles are given below.
∠1 = ∠3 = 40°
∠2 = ∠4 = 140°
The corresponding angles are given below.
∠1 = ∠5 = 40°
∠2 = ∠6 = 140°
∠3 = ∠7 = 40°
∠4 = ∠8 = 140°
Then the measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.
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What is the measure of 24 in the triangle shown?
32°
117°
22
148
The sum of three angles of a triangle is 180° . 32° is the angle at 24 when other two angles are 85° and 63°.
What is angle sum property?The sum of three angles of a triangle is 180° .
Given two angles of a triangle are 85° and 63°. We need to find the third angle at 24.
The angle at 24 be x.
By angle sum property,sum of three angles of a triangle is 180°.
The two angles are 85° and 63° and third angle is x.
85°+63°+x=180°
148°+x=180°
x=180°-148°
x=32°
Therefore the angle at 24 is 32° when other two angles are 85° and 63°.
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I need help with this question please, my exam is tomorrow.
Answer:
Center: (2,2)
Radius: 2
Answers:
Center = (2,2)
Radius = 2
=================================================
Explanation:
Consider (A+B)^2 = A^2+2AB+B^2 after using the FOIL rule.
If A = x, then we have (x+B)^2 = x^2+2Bx+B^2
The coefficient of the x term is 2B. It divides in half to get B, and it squares to B^2 as the final term.
In short, if we want to complete the square on something like x^2-4x, then we do two things:
Divide the x coefficient in halfSquare the resultSo we go from -4 to -2 after dividing in half, and then from -2 to 4 after squaring. We'll add 4 to both sides to complete the square for the x terms.
[tex]x^2+y^2-4x-4y+4 = 0\\\\(x^2-4x)+(y^2-4y)+4 = 0\\\\(x^2-4x+4)+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y)+4 = 4\\\\[/tex]
We'll do the same thing for the y terms. Though notice we already have a +4 on the left side. So we can have it absorb into the y terms parenthesis grouping like so
[tex](x-2)^2+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y+4) = 4\\\\(x-2)^2+(y-2)^2 = 4\\\\[/tex]
Now compare that to the circle template
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
We see that
h = 2k = 2r = 2This circle has its center at (h,k) = (2,2)
The radius is r = 2
-12x - 17 = -89
i neeeed help
Answer:
x = 6
Step-by-step explanation:
- 12x - 17 = - 89 ( add 17 to both sides )
- 12x = - 72 ( divide both sides by - 12 )
x = [tex]\frac{-72}{-12}[/tex] = 6
A diamond is purchased for $ 2500 . Suppose its value increases 5 % each year.
a. What is the value of diamond after 8 years?
Answer:
$3500
Step-by-step explanation:
x = value of diamond with an increase of 5% every year for 8 years
x= 2500(0.05)
x= 125(8)
x = 1000
2500 + 1000 = $3500
The value of the diamond after 8 years is the amount of $3693.63.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To find the value of the diamond after 8 years, we need to calculate the compound interest.
The formula for compound interest is:
A = P(1+r/100)ⁿ
here:
A = final amount
P = principal amount
r = annual interest rate (as a decimal)
t = time in years
Using this formula, we can calculate the value of the diamond after 8 years:
P = 2500
r = 5% = 0.05
t = 8
A = 2500 (1 + 0.05/1)¹ˣ⁸
A = 2500 (1.05)⁸
A = 2500 (1.4775)
A = $3693.63
Therefore, the value of the diamond after 8 years is $3693.63.
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Please answer the question and help me pass
Answer:
10 *6= 60
60÷2=30
1÷2×b×h formula
answer- 30
If w = 22, what is the value of 4w − 12?
Answer:
76
Step-by-step explanation:
Well just substitute 22 in for w. Multiply 4 time 22 that equals 88. Then just subtract 12 from 88, and you end up with your final answer of 76
Express 48 as sum of two odd prime
Answer:
19 , 29
Step-by-step explanation:
19 + 29 = 48
mark brainiest pls
What is the positive solution to this equation?
3x²+2x = 16
Enter your answer in the box.
X =
Answer: 2
Step-by-step explanation: There are two solutions: 2, and -8/3. 2 is the positive solution.
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Suppose one base angle of an isosceles triangle has a measure of 44°. What is the measure of the vertex angle?
a. 108°
b. 92°
c. 56°
d. 44°
The measure of the vertex angle is 92°
Here,
The triangle is isosceles and one base angle of an isosceles triangle has a measure of 44°
We have to find the measure of the vertex angle.
What is Isosceles triangle?
A triangle is said to be isosceles if there is any two corresponding sides are equal and there angle are equal.
Now,
The triangle is isosceles triangle.
Hence, there corresponding sides and there angles are equal.
So, Both base angles of a triangle are equal.
And, Sum of angles of a triangle are 180°
Let the measure of the vertex angle is x°
Hence,
⇒ 44° + 44° + x° = 180°
⇒ x° = 180° - 88°
⇒ x° = 92°
Therefore, The measure of the vertex angle is 92°
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Write an equation of the line through each pair of points in slope-intercept form.
(-12,-6) and (8,9)
The equation of line is:
y = (5/2) x - 11
Given,
Points (x₁, y₁) = (-12, -6) and (x₂, y₂) = (8, 9)
We can find the slope using the equation for slope
m = (y₂ - y₁) / (x₂ - x₁)
= (9 -(-6)) / (8-(-12))
= (9+6) / (8 + 12)
= 15/20 = 3/4
We know the slope and a point, so we can use point slope form to make an equation
y-y₁ = m(x-x₁)
y - (-6) = 3/4 (x-(-12))
Distribute
y+6 = 3/4x – 3/4 × 2
y+6 = 3/4x - 3/2
Add -6 to each side
y + 6 -6 = 3/4x - (3/2)-6
y = 3/4x - (-9/2)
y = 3/4x + 9/2
This is in slope intercept form (y= mx+b)
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The Americans with Disabilities Act requires that wheelchair ramps have at least a 12 -inch run for each rise of 1 inch.
b. The maximum length that the law allows for a ramp is 30 feet. How many inches tall is the highest point of this ramp?
The highest point of this ramp will be at 30 inches.
It is given that Wheelchair ramps have at least a 12 -inch run for each rise of 1 inch and Max length for a ramp is 30 feet.
We have to find the highest point of ramp in inches.
What will be the value of 10 feet in inches ?
As we know that 1 feet = 12 inches , the value of 10 feet in inches will be ; 10 × 12 inches or 120 inches.
As per the question ;
Wheelchair ramps have at least a 12 inch run for each rise of 1 inch.
Max length for a ramp = 30 feet
or
Max length for a ramp = 30 × 12 inches
or
Max length for a ramp = 360 inches
The highest point of this ramp will be at ;
= 360 ÷ 12
= 30 inches
Thus , the highest point of this ramp will be at 30 inches.
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A conditional statement has the same truth value as:
Contrapositive
Converse
, ,
Inverse
A conditional statement has the same truth value as Contrapositive
How to complete the statement?From the question, we are to determine which type of conditional statement has the same truth value as the original statement
As a general rule, if the truth value of an original statement is True, the truth value of the contrapositive would also be true
Similarly;
If the truth value of an original statement is false, the truth value of the contrapositive would also be false
Hence, a conditional statement has the same truth value as contrapositive
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a is directly proportional to square of c.
w is inversely proportional to a³.
When c = 49, a = 35
When a = 2, w = 16.
Find the value of w when c = 4.
In the given question the value of w is 0.128.
What do we mean by directly proportional?When two quantities are directly proportional, it means that if one increases by a certain percentage, the other increases by the same percentage. For example, as the cost of gasoline rises, so do food prices.So, w when c = 4:
a∝√ca = k√c35 = k×7k = 5a = 5√cNow,
w ∝ 1/k³w = k/a³16 = k/8k = 128w = 128/a³Then,
c = 4a = 5×√4 = 10a = 10w = 128/10³w = 0.128Therefore, in the given question the value of w is 0.128.
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Given that →s is < 2,-6> and →t is <-10,7> , find the component form of →s + →t
The component form of →s + →t is <-8, 1>
We know that the component form of a vector is the ordered pair that describes the changes in the x- and y-values.
In this question, we have been given two vectors
vector s = < 2, -6>
and vector t = <-10, 7>
We need to find the component form of →s + →t
→s + →t
= < 2, -6> + <-10, 7>
= <2 + (-10), -6 + 7>
= <2 - 10, 1>
= <-8, 1>
Therefore, the component form of →s + →t is <-8, 1>
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Example 4 PH00F Write a two-column proof of Theorem 4.3 .
The proof of Theorem 4.3 with an example is shown.
What is theorem 4.3?Third Angles Theorem: If two angles of one triangle are congruent with two angles of another triangle, then the third angles must be congruent as well.To prove Theorem 4.3:
Let,s take two triangles, that is △ABC and △ADC.
In which AC⊥BD so ∠ACB ≅∠ACD.As, AC bisects ∠A so, ∠BAC ≅ ∠DAC.Since two pairs of angles are congruent, then the △ABC≅△ADC is under AA condition.
Then, ∠B≅∠D under CPCT condition (corresponding parts of congruent triangles).Therefore, the proof of Theorem 4.3 with an example is shown.
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1/5 (15b - 7) = 3b – 9
Answer: -7/5=-9
Step-by-step explanation:
I hope it helps
Answer: - 7/5 = -9
Step-by-step explanation: Combine like terms into single fraction, multiple by 1, subtract 3, simply.
If x varies partly as y and partly as the square of y when y =2,x=5 bad when y=5,x=57.5 find x when y =4
The value of x when y = 4 is 0. 25
How to determine the valueFrom the information given, we have that;
x varies directly as yx also varies partly as y²This is expressed as;
x ∝ 1/ y²
x = y/y²
Let's substitute the value of y as 4 into the equation;
x = 4 / 4²
Find the square
x = 4 / 16
Find the ratio
x = 1/ 4
x = 0. 25
Thus, the value of x when y = 4 is 0. 25
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If DM = 35, what is the value of r? DG = r+2. GM = 2r-13.
Based on the given parameters, the value of r is 46/3
How to determine the value of r?
The given parameters are
DG = r + 2
GM = 2r - 13
DM = 35
This means that
DM = DG + GM
So, we have
r + 2 + 2r - 13 = 35
Evaluate the like terms
3r = 46
Divide both sides by 3
r = 46/3
Hence, the value of r is 46/3
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I WILL GIVE U EXTRA BRAINLY POINTS!!
i don't understand this please help :)
Two angles are supplementary is the measure of one angle is 54.3 degrees what is the measure of the other angle? Answer to the first decimal place, ie 79.5.
Answer: 125.7 degrees
Step-by-step explanation:
supplementary angles add up to 180 degrees.
angle 1 + angle 2 = 180
54.3+angle 2=180.0
54.3-54.3+angle 2=180.0-54.3
angle 2=180.0-54.3
angle 2=125.7 degrees
Find the simple interest paid on a 8 year loan
of $2764 at 12.25% interest
Answer: 1,585.12 is your interest. full is 4349.12
Step-by-step explanation: brainlist pls
Which equation has the variable, or missing number, in the correct place to match the given situation?
The Lerch family drove a total of 482 miles, starting on Friday and ending on Sunday. They drove 138 miles on Friday and 225 miles on Saturday. How many miles did they drive on Sunday?
From the total amount of miles driven, it is found the equation that matches the given situation is:
138 + 225 + x = 482.
Solving the equation, it is found that they drove 119 miles on Sunday.
How to find the total amount of miles driven?The total amount of miles driven is given by the addition of the number of miles driven on Friday, Saturday and Sunday.
The separate amounts are given as follows:
Friday: 138 miles.Saturday: 225 miles.Sunday: x miles.Total: 482 miles.Hence the equation that matches the given situation is:
138 + 225 + x = 482.
Solving the equation, we have that:
x = 482 - (138 + 225)
119.
They drove 119 miles on Sunday.
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What is the slope of the line that passes through the given points?
d. Use the slope formula to show in part (a) that it does not matter which point you choose for (x₁, y₁) .
Lets consider an example to to show that it does not matter which point you choose for (x₁, y₁) .
Let the points be -
(2,1) and (4,7)
where x1 and x2 are 2, 4
y1 and y2 are 1,7.
So the formula for slope will be -
m = y2 - y1 / x2 - x1
⇒ 7 - 1 / 4 - 2
⇒ 6 / 2
⇒ 3 .......(1)
So, the slope of the equation is 3 for x1, x2 = 2, 4 and y1, y2 = 1,7
Now, let us consider,
x2 = 2 and x1 = 4 , y1 = 7 and y2 = 1
m = 1 - 7 / 2 - 4
m = -6 / -2
m = 3 ...........(2)
From (1) and (2), we can infer that it does not matter which point you choose for (x₁, y₁).
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A bakery sells an average of 14 dozen cupcakes a day to about 50 customers. what is their average sale rate, in cupcakes per customer?
i also need the answer really quick!!!
The average sale rate is 3 cupcakes per customer.
What are mathematical operations?The principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action on each function.So, in 1 dozen there are 12 pieces.
Then,
14 × 12 = 168168/50 = 3.36After rounding off: 3 pieces per customerTherefore, the average sale rate is 3 cupcakes per customer.
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Sammie was looking for a dress to wear to the wedding. She found one that she liked for 20% off. To go along with it, she also purchased a necklace for $7.50. Which expression represents the amount Sammie spent?
The expression that represents the amount spent is 0.8x + 7.50
Which expression represents the amount Sammie spent?The given parameters are
Discount = 20%
Necklace = 7.50
Let the cost of the dress be x
So, the expression that represents the amount Sammie spent is
Expression = (1 - Discount) * x + Necklace
This gives
(1 - 20%) * x + 7.50
Evaluate
0.8x + 7.50
Hence, the expression that represents the amount spent is 0.8x + 7.50
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Determine the perimeter of a triangle with vertices defined by the given points to the nearest tenth. a(1,1),b(2,5),c(5,1)
A triangle with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1) has a perimeter of 13.1 units.
A triangle is a two-dimensional shape that has three sides or edges and three vertices.
Perimeter refers to the distance around any two-dimensional shape. The perimeter of a triangle is the sum of the length of its sides.
To solve for the perimeter of triangle ABC with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1), solve first for the length of each side, namely side AB, side BC, and side AC.
And to solve for the length of each side, use the distance formula given by:
d = √(x2 - x1)^2 + (y2-y1)^2
side AB : d = √(2 - 1)^2 + (5 - 1)^2 = √1 + 16 = √17 units
side BC : d = √(5 - 2)^2 + (1 - 5)^2 = √9 + 16 = √25 = 5 units
side AC : d = √(5 - 1)^2 + (1 - 1)^2 =√16 + 0 = √16 = 4 units
Solving for the perimeter of triangle ABC,
P = AB + BC + AC
P = √17 + 5 + 4
P = 4.123 + 9
P = 13.123 units
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If m angle EFH = (5x+1), m angle HFG = 62 degrees, m angle EFG = (18x+11), find each measure
The measure of each angles are 21 and 83degrees
Addition postulateA line is defined as the distance between two points while an angle is the point where two lines intersect.
From the diagram shown, the expression below is true;
<EFH + <HFG = <EFG
Substitute the given parameters to have:
5x+1 + 62 = 18x + 11
Collect the like terms
5x - 18x = 11 - 63
-13x = -52
x = 52/13
x = 4
Find each measure
<EFH = 5(4) + 1
<EFH = 21
degrees
<EFG = 18(4) +11
<EFG = 72 + 11
<EFG = 83 degrees
Hence the measure of each angles are 21 and 83degrees
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