Answer:The value of angle y is 40°.
Complementary angles are the angles that have their sum equal to 90°.
Therefore, based on the information given, the value of angle y will be calculated thus:
x + y = 90°.
4y - 110° + y = 90°
Collect like terms
4y + y = 90° + 110°
5y = 200°
y = 200/5
y = 40°
The value of angle y is 40°.
Step-by-step explanation:
(-50) ÷ what is -1, number in the blank will be
The function g(x) is shown on the graph.
What is the equation of g(x) in vertex form?
g(x) = (x − 4)2 − 3
g(x) = (x − 4)2 + 3
g(x) = (x + 4)2 − 3
g(x) = (x + 4)2 + 3
Answer:
The correct answer is g(x) = (x+4)2+3
Step-by-step explanation:
The graph is sifted 3 units up and 4 units left.
I need help with the graph about it increasing and decreasing!!
Answers:
Increasing: [tex](-1.5, 2)[/tex]
Decreasing: [tex](-\infty,-1.5) \cup (2,\infty)[/tex]
==================================================
Explanation:
A function curve is considered increasing when moving uphill as you move to the right.
We're going uphill on the interval [tex]-1.5 < \text{x} < 2[/tex] which translates to the interval notation [tex](-1.5, 2)[/tex]. Be sure not to confuse this with ordered pair notation which unfortunately looks identical. The curved parenthesis are used to exclude each endpoint.
-------------
When moving to the right, we go downhill on two separate regions:
When x < -1.5, aka [tex]-\infty < \text{x} < -1.5[/tex]When x > 2, aka [tex]2 < \text{x} < \infty[/tex]The first portion translates to the interval notation [tex](-\infty,-1.5)[/tex]
The second portion translates to [tex](2,\infty)[/tex]
We glue those regions together with a union symbol to get [tex](-\infty,-1.5) \cup (2,\infty)[/tex]
The union symbol basically means "or" when it comes to interval notation. So we are decreasing on the interval [tex](-\infty,-1.5)[/tex] or decreasing on the interval [tex](2,\infty)[/tex]
PZ HURRY 15 POINTS
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
4,225
3,380
3,127
3,042
It can be estimated that approximately 3,042 people in attendance would prefer ketchup on a hot dog.
Thus, the correct answer is 3,042.
To determine how many people in attendance would prefer ketchup on a hot dog based on the data from the sample, we need to calculate the proportion of people who prefer ketchup and apply it to the total attendance.
The sample indicates that out of 150 people surveyed:
54 people prefer ketchup
36 people prefer relish
60 people prefer chili
To find the proportion of people who prefer ketchup, we divide the number of people who prefer ketchup by the total number of people surveyed:
Proportion of people who prefer ketchup = 54 / 150 = 0.36
Now, to estimate the number of people in attendance who would prefer ketchup on a hot dog, we multiply the proportion calculated above by the total attendance:
Estimated number of people who prefer ketchup = 0.36 [tex]\times[/tex] 8,450 = 3,042
For similar question on estimated.
https://brainly.com/question/29071363
#SPJ8
Use the word bank to help identify each part of the quadrilateral.
word bank: base, leg, parallel, midsegment, angle, diagonal, side.
What is the solution of x-1/x^2 +5x+4 less than or equal to 0
Answer:
[tex]x-1/x^2 +5x+4[/tex] = no real value
Step-by-step explanation:
Step 1 : Multiply through by x^2
[tex]x^{2} -1 +5x^{3}+ 4x^{2}[/tex]
Step 2 : Collect like terms
[tex]5x^{3}+5x^{2} -1\geq 0[/tex]
Step 3 : Ignore the sign and solve for x
[tex]5x^{3} +5x^{2} -1 = 0\\x =0.380609458\\x= 0.4(2dp)[/tex]
Step 4 : Input back into the equation
Step 5: This shows that x-1/x^2 +5x+4 has no real values.
Find the sum of the first n terms
using the formula:
a(1-r^n)/1-r
1, 5/3, 25/9, 125/27, 625/81
This would be a big help
The total of the first four terms is thus 8/3.
What does sum mean?The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.
The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.
We enter these numbers into the formula to determine the sum of the initial n terms:
S(n) = [tex]a(1-r^n)/(1-r)[/tex]
S(n) = [tex]1(1-(5/3)^n)/(1-5/3)[/tex]
S(n) = [tex]3/2(1-(5/3)^n)[/tex]
So, we add n to this formula to get the sum of the initial n terms of a given sequence:
S(n) = [tex]3/2(1-(5/3)^n)[/tex]
For instance, we replace n = 4 to get the sum of the initial four terms:
S(4) = [tex]3/2(1-(5/3)^4)[/tex]
S(4) = 3/2(1-625/81)
S(4) = 3/2(144/81)
S(4) = 72/27
S(4) = 8/3
To know more about Sum visit:
https://brainly.in/question/48939038
#SPJ1
The total of the first four terms is thus 8/3.
What does sum mean?The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.
The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.
We enter these numbers into the formula to determine the sum of the initial n terms:
S(n) = [tex]a(1-r^{n} )/(1-r)[/tex]
S(n) = [tex]1(1-(5/3)^{n} /(1-5/3)[/tex]
S(n) = [tex]3/2(1-(5/3)^{n} )[/tex]
So, we add n to this formula to get the sum of the initial n terms of a given sequence:
S(n) = 3/2(1 - [tex](5/3)^{n}[/tex] )
For instance, we replace n = 4 to get the sum of the initial four terms:
S(4) = [tex]3/2(1-(5/3)^{4} )[/tex]
S(4) = 3/2(1-625/81)
S(4) = 3/2(144/81)
S(4) = 72/27
S(4) = 8/3
To know more about Sum visit:
brainly.com/question/13013054
#SPJ1
complete ques is:
Find the sum of the first n terms ( 1,2,3,4,5.......n)
using the formula:
a(1-r^n)/1-r
1, 5/3, 25/9, 125/27, 625/81
Find the volume of the composite figure.
Figure not drawn to scale
The volume of the two cuboid added together will be 192 cm³.
what exactly is a cuboid?
A cuboid, also known as a rectangular prism, is a three-dimensional solid shape that has six rectangular faces. It is a type of polyhedron, a geometric figure with flat faces and straight edges.
A cuboid has three pairs of congruent and parallel faces, with each pair being congruent to the other. These pairs of opposite faces are known as bases, and the other four faces are called lateral faces. The lateral faces are also rectangles and are perpendicular to the bases.
Now,
As Volume of the cuboid= L*B*H
where l=length, B=Breadth and H=Height
and volume of the figure =volume of 2 cuboids
=8*4*3+10*3*4
=72+120
=192 cm³
Hence,
The volume of the two cuboid added together will be 192 cm³.
To know more about cuboid visit the link
https://brainly.com/question/29424737
#SPJ1
Tom wishes to purchase a property that has been valued at $300,000. He has 25% of this amount available as a cash deposit, and will require a mortgage for the remaining amount. The bank offers him a 25-year mortgage at 2% interest. Calculate his monthly payments.
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer.
so hmmm 25% of that 300,000 is going as a downpayment, so he need the loan for the remaining 75% of that hmmm
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of 300000}}{\left( \cfrac{75}{100} \right)300000}\implies 225000[/tex]
so for that much, so since he'll be making monthly payments, the compounding period will be monthly, now, we're assuming the payments are at the end of each month.
[tex]~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Payments of an ordinary annuity}} \\\\ pmt=A\left[ \cfrac{\frac{r}{n}}{\left( 1+\frac{r}{n} \right)^{nt}-1} \right][/tex]
[tex]\begin{cases} A=\textit{accumulated amount}\dotfill &225000\\ pmt=\textit{periodic payments}\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]pmt=225000\left[ \cfrac{\frac{0.02}{12}}{\left( 1+\frac{0.02}{12} \right)^{12 \cdot 25}-1} \right] \\\\\\ pmt=225000\left[ \cfrac{\frac{1}{600}}{\left( \frac{601}{600} \right)^{300}-1} \right]\implies pmt\approx 578.67[/tex]
 Find the area of the shaded sector.
Answer In Exact Form (don't put pi in calculator, simplify your decimal answer to a fraction, and put pi symbol in answer).
The area of the shaded sector is equal to: A. 415π/2 ft².
How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.Substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = 332(π/180) × (15)²/2
Area of sector = 74,700π/180 × 1/2
Area of sector = 415π/2 ft²
Read more on arc length here: brainly.com/question/28108430
#SPJ1
Which statement correctly describes the value of the expression 8×7/9
A) less than 7/9
B) greater than 9
C) between 8 and 9
D) between 7/9 and 8
The value of the expression is between 7/9 and 8, since 7/9 < 56/9 < 8. So the correct option is D.
Describe Algebraic Expression?Algebraic expressions can represent real-world situations, formulas, and equations. They are commonly used in algebra, which is a branch of mathematics that deals with symbols and the rules for manipulating these symbols.
Algebraic expressions are important tools in solving equations and real-world problems that involve variables and unknowns. They are also used in calculus, physics, engineering, and other fields that require mathematical modeling and analysis.
The value of the expression 8×7/9 can be simplified using the order of operations (PEMDAS) as follows:
8×7/9 = (8×7)/9 = 56/9
Therefore, the value of the expression is between 7/9 and 8, since:
7/9 < 56/9 < 8
So the correct statement is: D) between 7/9 and 8.
To know more about expression visit:
https://brainly.com/question/29052794
#SPJ1
What is 24 and 816,000 equals blank divided by 10 to the fifth power
Answer: We have the equation:
24,816,000 = x / 10^5
To solve for x, we can multiply both sides by 10^5:
24,816,000 * 10^5 = x
Using a calculator or long multiplication, we can simplify this to:
2,481,600,000,000 = x
Therefore, 24,816,000 is equal to 2,481,600,000,000 divided by 10 to the fifth power.
Step-by-step explanation:
1. Solve: (6 + 3)2 – 17 × 3 + 70
The solution of this expression is 37
Numerical expressionsTo solve this, first calculate the operations in parentheses.
Then perform the other operations, following the order of resolution
[tex]\begin{array}{l}\sf (6 + 3)2-17\times 3 + 70\\\sf 9\times 2-51+ 70\\\sf 18-51+ 70\\\sf 88-51\\\therefore \bf 37\end{array}[/tex]
For this expression, the result is 37
See more questionbrainly.com/question/30991005
If you have any question about this solution, you can ask me in the comments :)
Two cross sections the same or different
Shape
Answer:same
Step-by-step explanation:because I said so
The demand for a product is given by p+5q= 380 or, q = (380-p)/5 and the supply for this product is given by p-3q = 172 or, q = (p-172)/3 The price at which the quantity demande
Answer:
The equilibrium price is $250.
The equilibrium quantity is 26 units.
Step-by-step explanation:
To find the equilibrium price, we need to find the price at which the quantity demanded equals the quantity supplied. This occurs when q (quantity demanded) equals q (quantity supplied).
So, we can set the two equations for q equal to each other:
(380-p)/5 = (p-172)/3
To solve for p, we can cross-multiply and simplify:
3(380-p) = 5(p-172)
1140 - 3p = 5p - 860
1140 + 860 = 8p
2000 = 8p
p = 250
Therefore, the equilibrium price is $250. We can plug this value back into either equation for q to find the equilibrium quantity.
Using q = (380-p)/5, we get:
q = (380-250)/5 = 26
So the equilibrium quantity is 26 units.
2. The back of Nico's truck is 7 feet long, 4 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 1 foot on each side. K How many boxes of papers can Nico pack into the back of his truck? Show your work. (Try drawing a picture of the back of the truck and how many boxes can stack in there to help you see the answer better. Possible extra credit for your drawing.) Answer:
Based on division operation, the number of boxes of papers that the back of Nico's truck can stack in is 224.
What is division operation?Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
Division operation involves the dividend divided by the divisor to produce a result known as the quotient.
In this situation, the volume of Nico's truck is determined as the dividend. The volume of each box of paper is determined as the divisor.
The result of the division operation is the quotient showing the number of boxes the truck can contain.
The length of Nico's truck = 7 feet
The width of Nico's truck = 4 feet
The height of Nico's truck = 8 feet
The volume that Nico's tuck can contain = 224 cubic feet (7 × 4 × 8)
= 224 feet³
The length of each box = 1 foot
The width of each box = 1 foot
The height of each box = 1 foot
The volume of each box of papers = 1 feet³ (1 × 1 × 1)
The number of boxes the truck can contain = 224 boxes (224/1)
Learn more about mathematical operations at https://brainly.com/question/4721701.
#SPJ1
Solve x2 – 18x + 81 = 4 by completing the square. Select any solutions that apply. A. x = –11 B. x = –7 C. x = 7 D. x = 11
The solutions to the equation x² - 18x + 81 = 4 by completing the square are x = 9 + 2i and x = 9 - 2i.None of the answer choices A, B, C, or D are correct.
What is an equation?An equation is a mathematical statement that shows the equality between two expressions, often containing variables and mathematical operations.
To solve the equation x² - 18x + 81 = 4 by completing the square, we can follow these steps:
x² - 18x + 77 = 0
Divide both sides by the coefficient of x² to make the coefficient 1:
x² - 18x + (81/1) = -77/1
x² - 18x + 81 = -77
Add the square of half the coefficient of x to both sides of the equation:
x² - 18x + (9)² = -77 + (9)²
x² - 18x + 81 = -4
(x - 9)² = -4
x - 9 = ±√(-4)
x - 9 = ±2i (where i is the imaginary unit)
x = 9 ±2i
To know more about coefficient visit:
https://brainly.com/question/1594145
#SPJ1
Helena wants to change the figure shown into two or more figures so she can
more easily find the area. Draw a line or lines to show what she could do. Then
write an expression for the area of each smaller figure. Write an expression for
the total area of the figure. Explain.
The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
What is the tοtal area?A sοlid οbject's surface area is a measurement οf the οverall space that the οbject's surface takes up. The tοtal area includes bοth the Carpet Area and Exclusive Areas as well as all οther lands within the Prοperty's perimeter bοrders.
Here, we have
Given: Helena wants tο change the figure shοwn intο twο οr mοre figures sο she can mοre easily find the area.
The figure is cοmpοsed οf a square and a rectangle. See the attached image.
Therefοre, yοu shοuld sum the area οf these geοmetric figures fοr determining the area οf the irregular figure.
Area οf the rectangle = bh.
The figure shοws that the sides fοr this rectangle are equal tο 4x-5 and (4x+3x). Then,
b = length οf the base= 4x-5
h = height = 4x+3x = 7x
A rectangle = bh = (4x-5)*7x = 28x²-35x
Area οf the square = l². The figure shοws that the sides fοr this square are equal tο 3x
l = length οf the side= 3x
Thus, A square = l² = (3x)² =9x²
We have tο find an expressiοn fοr the tοtal area οf the figure.
A tοtal= A rectangle+ A square
A tοtal= 28x²-35x+9x²
A tοtal= 37x²-35x
Hence, The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
To learn more about the total area from the given link
https://brainly.com/question/1293273
#SPJ1
The following are reasons to put your money in a saving account. (Check all that apply)
Money collects interest.
Get a rebate back in the mail.
Money is safe and insured.
The cοrrect respοnse is that mοney cοllects interest and mοney is safe and insured.
Why nοt explain interest?The fee yοu spend tο bοrrοw the mοney οr the fee yοu pay tο lend the mοney is called interest. Interest is frequently calculated as a yearly percentage οf the amοunt bοrrοwed. This percentage represents the lοan's interest rate.
The interest fοrmula is what?Interest equals P, R, and T is the fundamental interest fοrmula. P is the initial value (the beginning balance). Rate οf Interest, R (usually per year, expressed as a decimal). T is the sum οf all time frames (generally οne-year time periοds).
To know more about Interest visit:
https://brainly.com/question/30393144
#SPJ1
Refer to trapezoi EFGH WITH MEDIAN IJ if IJ=X,Hg=8 abd EF=12 what is the value of x
Answer:
x = 10
Step-by-step explanation:
A trapezoid is a quadrilateral with one pair of parallel sides.
The median of a trapezoid connects the midpoint of the non-parallel sides.
IJ is the median of the trapezoid. I is the midpoint of EH, and J is the midpoint of GF.
Also, the median of a trapezoid is also parallel to the parallel sides. IJ║ HG║ EF.
(The proof of this is extensive and requires drawing additional lines such as HJ and extending EF further until HJ and EF intersect at another point, Y. It is given as the other diagram. You also need prior knowledge of the midsegment of a triangle.)
The measure of the midsegment of a trapezoid, by definition, is also equal to the average of the measure of the parallel segments.
In the figure,
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
Substituting the values we have, HG = 8, EF = 12 gives us:
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
[tex]IJ=\dfrac{(8+12)}{2}[/tex]
[tex]IJ=\dfrac{20}{2}[/tex]
[tex]IJ=10[/tex]
IJ is 10 units.
What is entrepreneurs education
Answer: What an entrepreneur really is, though, is someone who runs their own business and takes a risk to do it.
Step-by-step explanation:
answered
Find the points on the line x=1
where the circle with equation
2x²+2y²-5x+7y-36-0 intersect
Answer: To find the points where the circle intersects the line x=1, we substitute x=1 in the equation of the circle:
2(1)² + 2y² - 5(1) + 7y - 36 = 0
Simplifying, we get:
2y² + 7y - 31 = 0
We can solve this quadratic equation by using the quadratic formula:
y = (-7 ± √(7² - 4(2)(-31))) / (2(2))
y = (-7 ± √225) / 4
y = (-7 ± 15) / 4
So the two possible values of y are:
y = 2 or y = -8/2 = -4
Therefore, the points where the circle intersects the line x=1 are (1, 2) and (1, -4).
Step-by-step explanation:
Help!!
Question
Triangle ABC is similar to triangle DEF. The length of BC¯¯¯¯¯ is 44 cm. The length of DE¯¯¯¯¯ is 14 cm. The length of EF¯¯¯¯¯ is 22 cm.
What is the length of AB¯¯¯¯¯?
Enter your answer in the box.
cm
The length of AB which is the missing length side of the similar triangles would be = 28 cm.
How to calculate the missing length of a triangle?To calculate the missing length of the triangle = AB , the scale factor should be determined.
The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.
The scale factor = dimensions of new object/ dimensions of original object.
A side of original = EF =22cm
A side of the new triangle = BC = 44
Scale factor = 44/22 = 2
Therefore the missing length of the new triangle = 14×2 = 28cm
Learn more about triangles here:
https://brainly.com/question/28470545
#SPJ1
The perihelion is?
The equation for the orbit of planet A around the sun is?
The perihelion is the point in a planet's orbit where it is closest to the sun.
The equation for the orbit of a planet around the sun depends on various factors, such as the shape of the orbit, the mass of the planet, and the gravitational force between the planet and the sun. Kepler's laws of planetary motion provide a framework for understanding the motion of planets in orbit, and the equations used to describe these orbits are generally based on these laws. The specific equation for the orbit of planet A would depend on the specific parameters of that planet's orbit.
A natural history museum surveyed the people visiting the museum for one month and created a circle graph to show the age of the visitors for that month.
If 5000 people visited the museum during the month the survey was taken, how many visitors were there for each age group?
Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
Will give brainliest
Steven sold 10 cabbages at K2.00 each, 20 heaps of kaukau at K5 each, and 10 heaps of potato at K3.00 each. What is Steven's total earning?
Answer:
K150
Step-by-step explanation:
10 x K2.00 = K20.00
20 x K5.00 = K100.00
10 x K3.00= K30.00
20+100+30= K150
Avani is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 38^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 46^{\circ} ∘ . If her eyes are 1.66 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
Answer:
Let's call the height of the antenna "h".
First, we can use the angle of elevation of 38^{\circ} ∘ to find the height of point A above the ground.
tan(38^{\circ}) = \frac{h}{21}
h = 21 \cdot tan(38^{\circ})
h \approx 15.6
So point A is approximately 15.6 meters above the ground.
Next, we can use the angle of elevation of 46^{\circ} ∘ to find the height of point B above the ground.
tan(46^{\circ}) = \frac{h}{d}
h = d \cdot tan(46^{\circ})
We can find the value of "d" using the Pythagorean theorem.
d^2 = 21^2 + 15.6^2
d \approx 25.7
So the distance from point A to point B is approximately 25.7 meters.
Finally, we can use the height of point A and the distance from point A to point B to find the height of point B (the height of the antenna).
h = d \cdot tan(46^{\circ})
h \approx 25.7 \cdot tan(46^{\circ})
h \approx 23.2
Therefore, the height of the antenna is approximately 23.2 meters.
Step-by-step explanation:
the scenario creates 2 right-angled triangles.
both have the same first leg : the horizontal distance from Avani's eyes to the building (21 m).
and both have a right angle (90°) at the point, where the horizontal distance meets the building.
the difference is now the second leg : the height of the building (starting at 1.66 m above ground), and the height of the building plus the height of the antenna (again starting at 1.66 m above ground).
another difference is the length of the line of sight (from Avani to AA, and from Avani to BB).
driving these differences is the difference in the angle at Avani (38° vs. 46°).
now, remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides of the triangle, A, B, C are the corresponding opposite angles of the triangle.
and remember : the sum of all angles in a triangle is always 180°.
what is the plan ?
we need to calculate the second leg of the larger triangle, and then the second leg of the smaller triangle and subtract that from the second leg of the larger triangle.
in other words :
(building + antenna) - building = antenna
so, we start with the larger triangle (up to BB).
the angle at Avani is 46°.
the angle at the building is 90°.
the angle at BB is then
180 - 90 - 46 = 44°.
21/sin(44) = (building + antenna)/sin(46)
(building + antenna) = 21×sin(46)/sin(44) =
= 21.74613659... m
now, for the smaller triangle (up to AA).
the angle at Avani is 38°.
the angle at the building is 90°.
the angle at AA is then
180 - 90 - 38 = 52°.
21/sin(52) = building/sin(38)
building = 21×sin(38)/sin(52) = 16.40699816... m
the height of the antenna is then again
(building + antenna) - building = 5.339138433... m
≈ 5.3 m
A toy company is building dollhouse furniture. A rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 3.5?
Answer: To find the perimeter of the door on a scale drawing, we need to first determine the dimensions of the door on the scale drawing.
If the actual height of the door is 7 centimeters, then the height on the scale drawing will be:
7 cm ÷ 3.5 = 2 cm
Similarly, if the actual width of the door is 3 centimeters, then the width on the scale drawing will be:
3 cm ÷ 3.5 = 0.857 cm
Now we can use these dimensions to find the perimeter on the scale drawing:
Perimeter = 2 × (height + width) = 2 × (2 cm + 0.857 cm) = 2 × 2.857 cm = 5.714 cm
Therefore, the perimeter of the door on the scale drawing is 5.714 centimeters.
If you have anymore questions, feel free to comment and I will help you.
Write the equation of the line that passes through the points (3, -4) and (7, 6). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answer:
Step-by-step explanation:
To write the equation of the line that passes through the points (3, -4) and (7, 6), we can follow these steps:
Step 1: Find the slope of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given values, we get:
slope = (6 - (-4)) / (7 - 3)
slope = 10 / 4
slope = 5 / 2
Step 2: Use point-slope form to write the equation of the line
Point-slope form of a line with slope m passing through a point (x1, y1) is given by:
y - y1 = m(x - x1)
We can use either of the given points to write the equation. Let's use (3, -4):
y - (-4) = (5/2)(x - 3)
Simplifying this equation, we get:
y + 4 = (5/2)x - (15/2)
Subtracting 4 from both sides, we get:
y = (5/2)x - (23/2)
This is the equation of the line in point-slope form.
Step 3: Simplify the equation if it is not in point-slope form
The equation we obtained in step 2 is already in point-slope form, so we do not need to simplify it any further.
Note: If the line was horizontal (i.e., it had zero slope), then its equation would be y = constant, where the constant is the y-coordinate of any point on the line. If the line was vertical (i.e., its slope was undefined), then its equation would be x = constant, where the constant is the x-coordinate of any point on the line.
Kira is installing a railing that is 35 inches above the ramp Let each be the height of the railing from the ground and all be the height of the ramp from the ground which equation represents the situation
Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let h be the height of the railing from the ground and let r be the height of the ramp from the ground.
We are given that the railing is 35 inches above the ramp, which means that the total height of the railing from the ground is h = r + 35.
So the equation that represents the situation is:
h = r + 35
Therefore, Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35
To learn more about Algebraic expression from given link.
https://brainly.com/question/953809
#SPJ1