The house is located 6.87 miles to the east of the cell tower.
What is Pythagoras theorem?“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given:
Let the center of the town represent the origin (0,0).
Also 1 unit = 1 mile.
Since the cell tower is located 3 miles east and 6 miles north of the center of a small town, it is represented by A(3, 6)
The cell tower has a coverage of radius 4 miles. This can be represented by a circle with equation:
(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius.
Then, (x - 3)² + (y - 6)² = 4²
(x - 3)² + (y - 6)² = 16
b) The house is 7 miles north. It can be represented by y = 5 line.
To find the distance east of the house we have to substitute y = 5 and solve for x,
(x - 3)² + (y - 6)² = 16
(x - 3)² + (5 - 6)² = 16
(x - 3)² + 1 = 16
(x - 3)² = 15
(x - 3) = ±3.87
x= 3 ±3.87
x= 6.87 or 0.87.
Hence, the house is located 6.87 miles to the east.
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6x(2x+3)+1(2x+3)
Rewrite the expression
Given:m<1+m<2=90 and m<3+m<4=90,prove m<1=m<4
The proof that the angles m<1 = m<4 is shown below
How to prove the measure of the anglesFrom the question, we have the following parameters that can be used in our computation:
Measure of angles
The angle measurements are then given as
m<1 + m<2 = 90 and m<3 + m<4 = 90
The relationship to prove is also given as
m<1 = m<4
Using the above as a guide, we have the following:
Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90
This gives
m<1 + m<2 = 90
-(m<3 + m<4 = 90)
Evaluate the difference
m<1 + m<2 = m<3 + m<4
When both sides of the angle equations are compared, we have:
m<1 = m<4
m<2 = m<3
Ignoring the second equation, we have
m<1 = m<4
Hence, the measure of the angles has been proved
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In triangle ABC, the measurement of angle A is is greater then the measurement of angle C, then BC> AC is this conditional true? If so, why?
Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.
What is the law of sines?We suppose a general triangle, for which:
Side with a length of a is opposite to angle of measure A.Side with a length of b is opposite to angle of measure B.Side with a length of c is opposite to angle of measure C.The lengths and the sine of the angles are proportionally related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The segments in this problem are given as follows:
BC opposite to angle A.AB opposite to angle C.Hence it can be affirmed that:
BC > AB.
As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.
As for segment AC, we need the measure of angle B, hence nothing can be affirmed.
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Goran wants to build a square picture frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?
After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.
What is a square?A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.
given,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.
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PLEASE HELP!
An architect is designing a circular window to be installed in the
gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?
Exact Circumference = 4pi feet
Approximate Circumference = 12.56 feet (when using pi = 3.14)
======================================================
Explanation:
The larger circle has a 3 foot radius.
The inner circle has a 3-1 = 2 foot radius.
Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.
C = 2pi*r
C = 2pi*2
C = 4pi
The exact circumference is 4pi feet. This is the perimeter around the circle.
If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.
Write an equation of the line passing through (- 5,5) and having slope - 4. Give the answer in slope-intercept form.
The equation of the line in slope-intercept form is:
Answer:
y = - 4x - 15---------------------------
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptPoint-slope form:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point on the lineUse the point-slope form to find the equation and then convert it to slope-intercept form:
y - 5 = - 4(x - (-5))y - 5 = -4(x + 5)y - 5 = - 4x - 20y = - 4x - 20 + 5y = - 4x - 15Please do 1. and 2.! 25 points, please need asap!
Step-by-step explanation:
1
We can see that RS divides ∆PQS into two equal parts
So,
PR = RQ
Therefore
RQ = 5.1
Now
PQ = PR + RQ
=> PQ = 5.1 + 5.1
=> PQ = 10.2
2
Here
KM is the angle bisector
So
JM = ML
JM = 46
3p-3p+2s-6s+2q-3q+8r-7r
Is it ok to not put the p in this equation as the 3p is minus
Answer:
- 4s - q + r
Step-by-step explanation:
that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-
⇒3p-3p+2s-6s+2q-3q+8r-7r
add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q
⇒0 - 4s - 1q + 1r
⇒- 4s - q + r Answer
hope that helps...
1.
(01.01 LC)
Subtract 28.9 − 9.25 =
19/65
(1 point)
2.
(01.01 C)
When adding 32.6 to a certain number, the sum is 36.14, as seen below. What number should go in the box to complete the addition problem?
The decimal 32.6 is added to an unknown whole number and 54 hundredths to equal 36.14.
(1 point)
36.14
3.
(01.02 LC)
Multiply 11.9 × 22.1. (1 point)
2.6299
2,629.9
262.99
26.299
4.
(01.03 LC)
What is the remainder when 16,055 is divided by 16? (Input numeric values only) (1 point)
10,03 and the remainder is 7
5.
(01.03 MC)
What is the quotient of 52.7 ÷ 4.25? (1 point)
1.24
12.4
13.28
132.8
6.
(01.05 MC)
Gracy has fraction 4 over 5 pound of bird seed. She needs fraction 3 over 10 pound to feed the birds daily. Which of the rectangle models below shows how many days' worth of seed Gracy has left? (1 point)
Rectangle model divided into five equal sections, four sections are labeled four-fifths and three sections are labeled three-tenths, equaling one and one-half days.
Rectangle model divided into ten equal sections, five sections are labeled four-fifths and three sections are labeled three-tenths, equaling one and two-thirds days.
Rectangle model divided into five equal sections, four sections are labeled four-fifths and two sections are labeled three-tenths, equaling two days.
Rectangle model divided into ten equal sections, eight sections are labeled four-fifths and three sections are labeled three-tenths, equaling two and two-thirds days.
7.
(01.06 HC)
Jessica used Fraction 2 over 3 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 3 over 4 yards of fabric, and why? (1 point)
Yes, because the quotient of Fraction 1 and 3 over 4 ÷ fraction 2 over 3 is 2 and 5 over 8
No, because the quotient of Fraction 2 over 3 ÷ Fraction 1 and 3 over 4 is 1 and 2 over 12
No, because the quotient of Fraction 1 and 3 over 4 ÷ fraction 2 over 3 is 1 and 2 over 12
Yes, because the quotient of Fraction 2 over 3 ÷ Fraction 1 and 3 over 4 is 2 and 5 over 8
8.
(01.07 MC)
A right rectangular prism has these dimensions:
Length − Fraction 1 and 1 over 4 units
Width − Fraction 5 over 8 unit
Height − Fraction 3 over 4 unit
How many unit cubes of side length Fraction 1 over 8 unit are required to pack the prism without any gap or overlap? (1 point)
60
75
150
300
9.
(02.01 MC)
A fish tank has black and white fish in the ratio of 2 to 6 as shown below:
2 black fish and 6 white fish are shown
Which is another ratio that can describe the black to white fish? (1 point)
1 to 5
5 to1
1 to 3
3 to 1
10.
(02.02 MC)
Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of water? (1 point)
one over ten
one over five
two over seven
two over five
11.
(02.03 LC)
Victor made different flags that had the same ratio of the length to the width. The table below shows the length and width of the flags Victor made:
Length (centimeter)
Width (centimeter)
3
2
6
4
9
6
12
8
?
10
The missing value in the table is
centimeters. (1 point)
12.
(02.03 MC)
The ratio of the number of cookies to the number of candies in different gift boxes is 5:7. Which table best shows the number of cookies and candies in different gift boxes? (1 point)
Cookies
Candies
5
12
10
24
15
36
Cookies
Candies
2
7
10
35
12
42
Cookies
Candies
10
14
15
21
20
28
Cookies
Candies
11
13
14
16
18
20
13.
(02.03 MC)
A printer printed 68 letters in 4 seconds. If it prints letters at a constant speed, it can print
letters in 30 seconds. (1 point)
For a science experiment, each student needs 5 grams of salt. If there are 26 students in the class how many milligrams of salt will they need?
2) Which of the following would be A' if A (2, -3)
was reflected over the x axis?
a. A'(-2, -3)
c. A'(-2, 3)
b. A'(2, 3)
d. A'(2, -3)
A'(-2, -3) would result if A (2, -3) was reflected over the x axis. Point (2,3)'s representation under the x-axis is (2,-3). from the y-axis P image (-a,b).
What is (2, -3) reflected over the x-axis?Changing the sign of the value on the opposite axis, in this case the y-value, is all that is required to reflect a point such as (-2,3) across the x-axis in a question. As a result, this location has a y-value of 3. A positive number, this. A negative sign produces a result of -3.
While the Y coordinate remains the same when you reflect across the Y-axis, the X coordinate changes sign. Determining the reflection of (2, 3) across the Y-axis is therefore (-2, 3). The Y-coordinate of each point must be negative while reflecting across the X axis, but the X value must remain constant.
Therefore the correct answer is option a ) A'(-2, -3)
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Need Help With This
Step-by-step explanation:
a) x+20+x+90=180 [sum of 3 angel of triangle]
2x + 110 = 180
2x = 180- 110
2x = 70
x = 70÷2
x = 35
b) 2y + y + y = 180
4y = 180
y = 180÷4
y= 45
c) 4z-30 + 2z = 180
6z = 180 + 30
6z = 210
z = 35
How do I even do thissss?
Please provide your question with a math problem in the form of an image or text.
A rectangular room measures 10 feet by 120 inches. Tonya said the area of the room is 1200 square feet. What did Tonya do wrong?
Answer: Tonya's calculation is incorrect because she mixed units of measurement. She used feet to measure one dimension of the room (10 feet) and inches to measure the other dimension (120 inches) and then calculated the area as 10 x 120 = 1200 square feet.
Area is a measure of the amount of space inside a two-dimensional shape, and it's typically measured in square units. To calculate the area of a rectangular room, you multiply the length of the room by the width of the room,
However in this case, Tonya used different units of measurement for length and width (feet and inches), and therefore the answer is incorrect.
You would need to convert inches to feet before multiplying 10 feet by 120 inches to get the area.
120 inches = 10 feet
So, the correct calculation of the area would be 10 feet * 10 feet = 100 square feet
It's worth mentioning that before calculating any area or volume, it's important to make sure that all units of measurement are consistent and the same.
Step-by-step explanation:
Please need help ASAP, 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!
Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed.
(1). ΔIJH ≅ ΔKHJ, by SSS criterion,
and (2) we need, ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove ΔTNS ≅ ΔUHS, by HL criterion.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the triangle:
ΔIJH ≅ ΔKHJ.
To prove the congruent by SSS:
We have to show that three sides of the triangle are congruent to three sides of the other triangle.
Here,
IJ ≅ KH.
IH ≅ JH, Given.
And both triangles share the same side JH.
So,
JH ≅ JH
So, ΔIJH ≅ ΔKHJ, by SSS criterion.
ΔTNS ≅ ΔUHS.
To prove the congruent by HL:
We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.
So, we need;
ΔTNS and ΔUHS are right-triangles.
S is the mid-point.
So,
SN ≅ SH.
ST ≅ US
So, ΔTNS ≅ ΔUHS, by HL criterion.
Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;
ΔTNS and ΔUHS are right-triangles and S is the mid-point.
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Aubree and Bo own competing taxicab companies. Both cab companies
charge a one-time pickup fee for every ride, as well as a charge for each mile
traveled. The equation y = 2.6x + 2.5 represents what Bo's company
charges. The table below represents what Aubree's company charges.
Aubree's Taxicab Company
Miles (x) Total Cost (y)
2
$7.50
4
$13.50
$19.50
$25.50
6
8
Use the dropdown menu and answer-blank below to
form a true statement.
Aubree's company charges $| less per mile than Bo's.
On solving the provided question we cans ay that - here in linear equation, y = 3 and x = -1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y = 2x + 1 - linear equation.
value of y;
[tex]x = 0\\y = 2(0) + 1\\y = 2 + 1\\y = 3[/tex]
value of x;
[tex]y = 0\\0 = 2x + 1\\2x = -1\\x = -1/2[/tex]
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How do I write an equation for this relationship (where y represents the number of blocks and x represents the stage number).
The equation of the line is y = 4x + 1 , where the slope of the line is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of blocks be y
Let the stage number be x
Let the first point be represented as P = P ( 1 , 5 )
Let the second point be represented as Q = Q ( 2 , 9 )
Now , the slope of the line between the points be
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 5 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 4 ( x - 1 )
On simplifying the equation , we get
y - 5 = 4x - 4
Adding 5 on both sides of the equation , we get
y = 4x + 1
Therefore , the value of A is y = 4x + 1
Hence , the equation of line is y = 4x + 1
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The length of a rectangle is twice its width. The perimeter is 30. Find it’s dimensions.
Answer:
Length = 10 Width = 5Step-by-step explanation:
Let's assume that,
→ Length = 2x
→ Width = x
→ Perimeter = 30
Perimeter of rectangle formula,
→ P = 2(L + W)
Now the value of x will be,
→ P = 2(L + W)
→ 2(2x + x) = 30
→ 2 × 3x = 30
→ 6x = 30
→ x = 30/6
→ [ x = 5 ]
Then required dimensions are,
→ Length = 2x = 2 × 5 = 10
→ Width = x = 5
Hence, these are the dimensions.
Length = 10
width = 5
Given-
Perimeter =30
l=2b........................................................ i
so
P =2(l+b)
here
30 = 2(2b +b)... ... .............. as l=2b from i
30 = 2*3b
30 = 6b
b= 5
which implies l= 2*5 --->10............................................ from i
so
Length = 10
width = 5
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Find X and Y - 20 POINTS
Check the picture below.
What is the following sum?
Answer:
The 4th one
Step-by-step explanation:
Right on edge!
Your company is considering a new project that will require $250,000 of new equipment at the start of the project. The equipment will have a depreciable life of eight years and will be depreciated to a book value of $10,000 using straight-line depreciation. The cost of capital is 12 percent, and the firm's tax rate is 21 percent. Estimate the present value of the tax benefits from depreciation.
The present value of the tax benefits from depreciation which is a non cash expenditure under capital budgeting decisions is $10432.80
What is Depreciation?According to the prudence concept of accounting convention, Depreciation is a non cash expenditure that has been charged against the profit. Depreciation is value that amortized over useful life of tangible fixed asset. The absolute decline in the value of asset due to obsolesce, usage of asset, wear & tear of fixed asset is referred as depreciation.
As per accounting standard on property, plant & equipment depreciation can be computed by straight line method and written down value method.
While analyzing the capital budgeting decision from the equipment to be acquired the cash inflows and outflows during the currency of the project shall be accounted for.
The tax benefit from depreciation expenses will be consider as cash inflow. The same shall be calculated by the present value annuity factor for the as follows:
cost of capital = 12 %
Depreciation = $10000
Life of the project = 8 years
Tax rate = 21%
Present value annuity factor (PVAF) at 12% for 8 years will be:
0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404
Grand total of the (PVAF) at 12% = 4.968
Now multiply the PVAF with depreciation amount
Present Value of Depreciation = 4.968 × 10000 = $49,680
Tax benefit from depreciation = $49,680 × 21% = $10432.8
Thus the tax Tax benefit from depreciation is $10432.80
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Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
The rate of change of surface area is 524.02 square kilometers per minutes.
what is surface area of square prism?The total space occupied by a three-dimensional square prism is called surface area.
What is the rate of change of surface area of the prism?
Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min
the increasing rate of height with respect to time, dh/dt = 10 km/min
At a time, t, base side, s = 4 km
and height, h = 9 km
we need to determine the rate of change of surface area with respect to time, d A/dt
from the differentiation chain rule, d A/ dt = d A /dt × ds /ds
d A /dt = d A/ ds × ds /dt ... equation 1
we know that the surface area for prism, A = 2s² + 4sh
if we differentiate with respect to s then we find d A /ds
d/ds (A) = d/ ds (2s² + 4sh)
d A /ds = 4s + 4h +4s dh/ds ...... equation 2
now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]
dh/ds = dh/ dt× dt/ds
d h/ ds = dh/dt × 1/ ds/dt
it stated earlier that dh/ dt = 10 and ds /dt = 7
dh / ds = 10/7
putting this value in equation 2, we get
d A /ds = 4s +4h + 4s ×10/7
as we know at time t, s= 4 and h = 9
d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7
d A /ds = 74.86
putting the value d A /ds in equation 1, we get
d A /dt = d A /ds × ds/ dt
d A/ dt = 74.86 × 7
d A /dt = 524.02 km² / min
hence, the rate of change of surface area = 524.02 square kilometers per minutes
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Ed is using the recipe shown to make fruit salad. He wants to use 30 diced strawberries in his fruit salad. How many bananas, apples, and pears should Ed use in his fruit salad?
Fruit Salad Recipe - 4 bananas, diced. 3 apples, diced. 6 pears, diced. 10 strawberries, diced.
Answer:
12 bananas
9 apples
18 pears
Step-by-step explanation:
You are tripling the recipe.
10 x 3 = 3
4 x 3 = 12
3 x 3 = 9
6 x 3 = 18
If s is directly proportional to t, and s = 30 when t = 15, find t when s = 64.
Step-by-step explanation:
please refer to sketch for detail
За – 29 = 3(a – 3).
Answer:
No Solutions
Step-by-step explanation:
Hello!
We can solve for a by isolating the variable.
Solve for a:Distribute: 3a - 29 = 3(a) - 3(3)Simplify: 3a - 29 = 3a - 9Subtract 3a from both sides: -29 = -9Since -29 cannot be equal to -9, there are no solutions for this equation.
For Exercises 13-17, given A(6,-4), B(3, 8), and
C(-7, 9), determine the coordinates of the vertices
of AA'B'C' for each glide reflection. Suppose p is
the line with equation x = -3,q is the line with
equation y = 9, and r is the line with equation
y=-2. SEE EXAMPLE 3
Answer
A(-10, 9), A'(-4, 9)
B(-4, 2), B'(-10, 2)
C(-7, 9), C'(-7, -4)
Example 3:
A(-3, 5), A'(3, 5)
B(-3, 0), B'(3, 0)
C(-3, 5), C'(-3, -10)
Find the sum of the first 12 terms of the geometric series
2 + 4 + 8 +...
In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.
How can the sum of the initial terms in a geometric series be determined?the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.
What is a geometric series term?A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.
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Bookerville has a record of 12 inches of rain in 5 days. How much will it have to rain on Friday to beat the record by one tenth of an inch
The amount of rain required would be 2.5 inches.
What is the addition?
Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.
To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.
Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.
So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches
Hence, the amount of rain required would be 2.5 inches.
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Find the distance between the points.
(-6,5),(-6,-3.5)
The distance is
Answer:
8.5
Step-by-step explanation:
there's a rule to get the distance between 2 points
√((1st x- 2nd x)²+(1st y- 2nd y)²)
√((-6-(-6))²+(5-(-3.5))²)
=√((-6+6))²+(5+3.5))²)
you can just type that on your calculator and you'll get the result
√((-6+6))²+(5+3.5))²)
=√((5+3.5))²)
= √((8.5))²)
the root goes away with the power (exponent)
so it equals 8.5
Find x, y, mzC, and mA' given m/A = y;
m/A' = 2x + 5, mc-3x-y,
mZC' = 4
The value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.
What is the triangle translation?
In mathematics, a triangle translation refers to the geometric transformation in which a triangle is moved to a new position without rotating or scaling it. The triangle is simply slid along a straight line in a certain direction, and the new position of the triangle will be parallel to the original one.
Given that ΔABC translates to ΔA'B'C', we can assume that the measures of the angles are the same in both triangles. Therefore, if we know the measure of an angle in one triangle, we can assume that the measure of the corresponding angle in the translated triangle is the same.
Given:
m∠A = y
m∠A' = 2x + 5
m∠C = 3x-y
m∠C' = 4
Since opposite angles in a rectangle are congruent, m∠A=m∠C' and m∠C = m∠A'
Therefore,
y = 4
3x-y = 2x + 5
Solving this equation gives us:
x = y + 5 = 4 + 5 = 9
y=4
m∠C = 3x - y = 3(9) - 4 = 25
m∠A' = 2x + 5 = 2(9) + 5 = 23
Hence, the value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.
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