Answers
Answer:
Step-by-step explanation:
We have 3 triangles here, all of them right triangles. The first one is the biggest one, triangle ABC. We know the side length AB = 14, and we know the hypotenuse length, BC = 30. We can use that, along with Pythagorean's Theorem, to solve for side length AC:
[tex]30^2=14^2+(AC)^2[/tex] and
[tex]900-196=(AC)^2[/tex] and
[tex]704=(AC)^2[/tex] so
[tex]AC=8\sqrt{11}[/tex]
We also have the smallest right triangle, triangle ABD, which has the base of x, our unknown. Side BD is our unknown, length x; side AD is the height, length y (also unknown); and side AB is the hypotenuse, length 14. We will come up with a system of equations for these 2 right triangles, using Pythagorean's Theorem, and then solve for x using substitution.
For the medium-sized triangle. triangle ADC, the hypotenuse is side AC with a measure of 8√11, the height is side AD length y, and the base is side DC length 30 - x. Putting those values into Pythagorean's Theorem:
[tex](30-x)^2+y^2=(8\sqrt{11})^2[/tex] and
[tex]900-60x+x^2+y^2=704[/tex] and
[tex]x^2-60x+y^2=-196[/tex]*** That's starred because it's important and we will come back to it.
The smallest triangle in Pythagorean's Theorem:
[tex]14^2=x^2+y^2[/tex] and solving that for y-squared:
[tex]y^2=196-x^2[/tex]. We will now sub that value for y-squared into the starred equation for y-squared and solve for x:
[tex]x^2-60x+196-x^2=-196[/tex] and
-60x = -392 so
x = 6.5
Related Questions
Calculate the amount of money you'll have at the end of the indicated time period.
You invest $1000 in an account that pays simple interest of 6% for 30 years.
The amount of money you'll have at the end of 30 years is $
Answers
Step-by-step explanation:
Simple Interest = PTR/100
=1000* 30* 6/100
=1800.
Amount= Principal + Interest
= 1000+1800
= $2800
The amount of money that has at the of 30 years is $2800.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year, the principal amount in simple interest remains constant.
As per the given,
Principle amount P = $1000
Rate of interest R = 6%
Time span T = 30 years.
Total amount = Principle amount + Interest
Total amount = P + (PRT)/100
Total amount = $1000 + (1000 x 6 x 30)/100
⇒ $2800
Hence "The amount of money that has at the of 30 years is $2800".
For more about simple interests
https://brainly.com/question/25845758
#SPJ5
Alex, Isaac and Mitch shared a cake. Alex ate 2\5 of the cake, Isaac ate 1/3 of the cake and Mitch ate the rest. What fraction of the cake dis Mitch ate?
Answers
Answer:
4/15
Step-by-step explanation:
f(x) = -3(x-1) find f(o).
Answers
Answer:
f(0) = 3
Step-by-step explanation:
Step 1: Distribute
f(x) = -3x + 3
Step 2: Plug in
f(0) = -3(0) + 3
f(0) = 3
Answer:
f(0) = 3
Step-by-step explanation:
f(x) = -3(x-1)
Put x as 0 and solve.
f(0) = -3(0-1)
Solve the brackets.
f(0) = -3(-1)
Multiply both terms.
f(0) = 3
I don’t know how to solve help pls
Answers
Answer:
The measure of angle a is 43 degrees.
Step-by-step explanation:
Angle P is congruent to Angle R. A triangle's angles add up to 180 degrees. 47*2=94. 180-94=86 degrees. 86/2=43 degrees.
Answer: 43°
Step-by-step explanation:
The degree of a triangle adds up to 180. We are given an angle of 47 and there is a right angle of 90
We now have 90 + 47 + a = 180
137 + a = 180
a = 43
Find the value of the unknown in the equation 4p + 2 = 8
a) p = 0
b) p = 2.3
c) p = 1.5
d) p = 4
Answers
Answer:
Option C
Step-by-step explanation:
=> 4p + 2 = 8
Subtracting 2 to both sides
=> 4p = 8-2
=> 4p = 6
Dividing both sides by 4
=> p = 1.5
Answer:
The answer is C.
Step-by-step explanation:
First, you have to subtract 2 to both sides :
[tex]4p + 2 = 8[/tex]
[tex]4p + 2 - 2 = 8 - 2[/tex]
[tex]4p = 6[/tex]
Next, you have to divide it by 4 :
[tex]4p = 6[/tex]
[tex]p = 6 \div 4[/tex]
[tex]p = 3 \div 2[/tex]
[tex]p = 1.5[/tex]
Heeeeelllpppp meeeeee!!!!
Look at the picture to answer this question!
Answers
Answer:
A. 72
Step-by-step explanation:
Determinant of a 2x2 matrix: ad - bc
In that case,
24(18) - 30(12)
432 - 360
72
And we have our answer.
Write 5.1 x 10 to the power of one as an ordinary number.
Answers
Answer:
51
Step-by-step explanation:
Multiplying 5.1 by 10^1 shifts the decimal point 1 place to the right. We get 51.
Factor 60 y − 90 − 20 x 60y−90−20x60, y, minus, 90, minus, 20, x to identify the equivalent expressions. Choose 2 answers: Choose 2 answers: (Choice A) A 5 ( 14 y − 16 − 4 x ) 5(14y−16−4x)5, left parenthesis, 14, y, minus, 16, minus, 4, x, right parenthesis (Choice B) B 2 ( 30 − 45 − 10 ) 2(30−45−10)2, left parenthesis, 30, minus, 45, minus, 10, right parenthesis (Choice C) C 5 ( 12 y − 18 − 4 x ) 5(12y−18−4x)5, left parenthesis, 12, y, minus, 18, minus, 4, x, right parenthesis (Choice D) D 10 ( 6 y − 9 − 2 x ) 10(6y−9−2x)
Answers
Answer:
D. 10(6y - 9 - 2x)
Step-by-step explanation:
We want to factor 60y - 90 - 20x.
We simply have to find the Highest Common Factor of the three numbers and factorize that out of the expression.
10 is common among all three:
10(6y - 9 - 2x)
We have factored it.
Answer:
c
d
Step-by-step explanation:
what is the graph of y > x2-9.
Answers
Answer:
The 1st graph
Step-by-step explanation:
When you graph the equation in a graphing calc, you should be able to see that the graph most similar would be the 1st one.
what is the solution to the equation 13 3/4 + x equals 7 1 / 4
Answers
Answer:
x=-6.5
Step-by-step explanation:
[tex]7\frac{1}{4} - 13\frac{3}{4}=-6\frac{1}{2}=-6.5[/tex]
What is 40% of 260..
Answers
Answer:
104
Step-by-step explanation:
40 x 260 /100 = 104
Answer:
104
Step-by-step explanation:
40% of 260=
40/100 x 260=
10400/100=
104
Work out the surface area of this cylinder
8.2 cm
17.5 cm
Answers
Answer: 1324.12 sq. cm.
Step-by-step explanation:
A=2πrh+2πr2
A = 2π x 8.2 x 17.5 + 2π x 8.2^2
A = 2π x 143.50 + 2π x 67.24
A= 1324.12
Answer:
SA = 1324.1 cm²
Step-by-step explanation:
Surface Area of Cylinder = [tex]2\pi rh+2\pi r^2[/tex]
Where r = 8.2 cm, h = 17.5 cm
=> SA = [tex]2(3.14)(8.2)(17.5)+2(3.14)(8.2)^2[/tex]
=> SA = [tex]901.6+2(3.14)(67.24)[/tex]
=> SA = 901.6 + 422.5
=> SA = 1324.1 cm²
.- Calcule el interés producido por un capital de 4 500 dólares al 5% de interés simple anual en 8 meses.
Answers
Answer: $150
Step-by-step explanation:
Hi, the question says:
Calculate the simple interest produced by $4500 at 5% simple annual interest in 8 months.
To answer this question we have to apply the simple interest formula:
I = p x r x t
Where:
I = interest
P = Principal Amount
r = Interest Rate (decimal form)
t = years
Since 1 year = 12 months;
For 8 months:
8/12 = 2/3 years
Replacing with the values given
I = 4500 x (5/100) x 2/3
I = $150
Feel free to ask for more if needed or if you did not understand something.
Can you help me with this question
Answers
Answer:
-1.67
Step-by-step explanation:
(8x - 4)(7y + 2) multiplying binomials
Answers
Step-by-step explanation:
8x(7y+2)-4(7y+2)
=56xy+16x-28y-8
Answer:
56xy+16x-28y-8
Step-by-step explanation:
you have to use the FOIL method to solve this is problem which is
F-First
O-Outer
I-Inner
F-Last
95 students choose to attend one of three after school activities: footbal,l tennis or running. There are 28 boys. 38 students choose football, of which 26 are girls. 23 students choose tennis. 29 girls choose running. A student is selected at random. What is the probability this student choose running? Give your answer in its simplest form.
Answers
Answer:
34/95
Step-by-step explanation:
Since 38 students choose football and 23 students chose tennis, then 95 - 38 - 23 = 34 students chose running. The probability is 34 / 95.
A hot-air balloon is flying at an altitude of 2999 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 34degrees, how far is the house from the pilot?
Answers
Answer:
5668.3
Step-by-step explanation:
The problem can be represented as a right angled triangle as shown below.
The angle of depression is equivalent to the angle inside the triangle (alternate angles) and it is 34°.
The altitude of the balloon is 2999 feet. (opposite)
Using trigonometric function, SOHCAHTOA, we can solve this:
[tex]sin(34) = \frac{opposite}{hypotenuse}\\ \\sin(34) = \frac{altitude}{distance}\\\\sin(34) = \frac{2999}{distance}\\\\distance = \frac{2999}{sin34}\\\\distance = 5668.3 feet[/tex]
The pilot is 5668.3 feet far away from the house.
Each term in the sequence below is 9 more than 1/3 the previous term. What is the value of y-x?
81, 36, x, y,...
Plz explain
Answers
Answer:
y - x = - 5
Step-by-step explanation:
Applying the rule gives
x = [tex]\frac{1}{3}[/tex] × 36 + 9 = 12 + 9 = 21
y = [tex]\frac{1}{3}[/tex] × 21 + 9 = 7 + 9 = 16
Thus
y - x = 16 - 21 = - 5
Find the 8th term of geometric sequence 2,-10,50...
Answers
Answer:
- 156250
Step-by-step explanation:
Find the ratio of the geometric sequence.
-10/2 = -5
50/-10 = -5
The common ratio is -5.
Apply the formula.
an = ar^(n-1)
Where a is the first term and r is the ratio.
a8 = 2(-5)^(8-1)
a8 = 2(-5)^7
a8 = 2(-71825)
a8 = -156250
Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6. If the solution region represents the number of hammers and wrenches that Brody can buy given his budget, determine which graph represents the solution set to the system of inequalities representing this situation. A. B. C. D.
Answers
Answer:
For this case, the first thing we must do is define variables:
x: number of hammers
y: number of wrenches
We write the system of inequations:
10x + 6y <= 120
x + y> = 14
Step-by-step explanation:
I need help, please Will mark the Brainliest
Answers
Answer:
A= BEP and BCG
Because they aree the only triangle
C= about 600 to 750
Step-by-step explanation:
Write 14/√2 + √50 in the form b√2 where b is an integer.
Answers
Answer:
[tex]12 \sqrt{2} [/tex]
Step-by-step explanation:
Taking the terms one at a time,
[tex] \frac{14}{ \sqrt{2} } \\ \frac{14 * \sqrt{2} }{ \sqrt{2} * \sqrt{2} } \\ \frac{14 \sqrt{2} }{2} \\ 7 \sqrt{2} [/tex]
[tex] \sqrt{50} \\ \sqrt{25 * 2} \\ \sqrt{25}* \sqrt{2} \\ 5 * \sqrt{2} \\ 5 \sqrt{2} [/tex]
Adding the terms, you have;
[tex]7 \sqrt{2} + 5 \sqrt{2} =(7 + 5) \sqrt{2} = 12 \sqrt{2} [/tex]
Hope it helps!
I'm out!
Answer:
12
Step-by-step explanation:
14/√2 +√50= 14*√2/√2*√2+ √25*2= 7√2+5√2= 12√2
12√2= b√2
b=12
Given the following diagram, find the missing measure. Given: PM MO m 2 = 30°, m P = 30 120 60 90
Answers
Answer:
60
Step-by-step explanation:
The sum of interior angles in a triangle is 180
180-90-30=60
How can you solve for x in the proportion StartFraction 7 over 8 EndFraction = StartFraction x over 24 EndFraction?
Answers
Answer:
21
Step-by-step explanation:
7/8 = x/24
Cross multiply.
8x = 24 × 7
8x = 168
x = 168/8
x = 21
Answer:
answer is d
Step-by-step explanation:
You drive an average of 750 miles per week in a car that gets 28 miles per gallon. With gasoline prices at $3.40 per gallon, what would be the difference in total weekly cost of gasoline if you start driving an SUV that gets 20 miles per gallon?
Answers
Answer:
$36.41/week
Step-by-step explanation:
Divide 750 miles/wk by 28 MPG -> = 26.79 gallons/week (I rounded.)
Divide 750 miles/wk by 20 MPG -> = 37.50 gallons/week
Car -> 26.79 gallons x $3.40 = $91.09
SUV -> 37.50 gallons x $3.40 = $127.50
$127.50 - $91.09 = Difference of $36.41/week
The difference in the total weekly cost of gasoline is $36.43 if you drive an average of 750 miles per week.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
You drive an average of 750 miles per week in a car that gets 28 miles per gallon. With gasoline prices at $3.40 per gallon.
For the first car:
Total number of miles = 750 miles
The gasoline prices at $3.40 per gallon
The car that gets 28 miles per gallon
Number of gallons used = 750/28 = 26.785
The total price of the gallon used = 26.785x3.40 = $91.07
For the SUV car:
Total number of miles = 750 miles
The gasoline prices at $3.40 per gallon
The car that gets 20 miles per gallon
Number of gallons used = 750/20 = 37.5
The total price of the gallon used = 37.5x3.40 = $127.5
The difference in total weekly cost of gasoline = 127.5 - 91.07 = $36.43
Thus, the difference in the total weekly cost of gasoline is $36.43 if you drive an average of 750 miles per week.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
PLS HELP I AM STUCK!!! 10^2+4-18+2-7*5-1
Answers
Answer:52
Step-by-step explanation:
Use pemdas :D
10^2+4-18+2-7*5-1
100+4-18+2-(7)(5)-1
104-18+2-(7)(5)-1
86+2-(7)(5)-1
88-(7)(5)-1
88-35-1
53-1
52
THE ANSWER TO YOUR PROBLEM!
52
THE ANSWER TO THE ANSWER TO YOUR PROBLEM!
10^2=100
10^2+14=114
10^2+4-18=86
10^2+4-18+2=88
10^2+4-18+2-7=81
10^2+4-18+2-7*5=83
10^2+4-18+2-7*5-1=52!
Hope i helped!-Animefan28
Which relationships have the same constant of proportionality between yyy and xxx as the equation 3y=27x3y=27x3, y, equals, 27, x?
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
y=9xy=9xy, equals, 9, x
(Choice B)
B
2y=18x2y=18x2, y, equals, 18, x
(Choice C)
C
pls answer as fast as u can
Answers
Answer:
3,12,15
Step-by-step explanation:
caculator
Triangle ABC has one side equal to 10 inches and one side equal to 7 inches. What could be the area of the triangle? I. 25 square inches II. 35 square inches III. 40 square inches
Answers
Answer: 35 square inches
Step-by-step explanation:
Area of triangle = (l * w) / 2
Multiply
10 * 7 = 70
Divide by 2
70 / 2 = 35
Answer:
35 square inches
Step-by-step explanation:
area=base times height divided by one-half
7x10=70
70/2=35
Find the 87th term of the arithmetic sequence –19, -13, -7,...
Answers
Answer:
87th term is 497
Step-by-step explanation:
first, you have to find the nth term:
figure out the difference between your set of numbers (in our case +6)
that means that is 6n. next, the nth term is basically the 0th term so you have to find the 0th term. all you have to do is do the inverse of 6n (-6n or -6), which gives us -25.
nth term= 6n-25
now replace n with 87.
final step:
87*6 (6n and n=87) and that gives you 522. then, you have to do 522-25, due to the equation. 522-25=497
497 is your 87th term.
Answer:
-535Step-by-step explanation:
[tex]a = -19\\d = T_{2} -T_{1} \\d = -19-(-13)\\d = -19+13\\d = -6\\T_{n}= a+(n-1)d \\\\T_{87} = -19+(87-1)-6\\T_{87} = -19+(86)*-6\\T_{87} = -19-516\\T_{87} = -535[/tex]
Reflect triangle a in the x axis to give triangle b. Then rotate your triangle b 90 degrees clockwise around the origin to give triangle c. Describe fully the single transformation that maps triangle a onto c
Answers
Answer:
The single transformation that maps a onto c is the reflection of the triangle a about the line y = -x
Step-by-step explanation:
To answer the question, we note that the result of reflection of a point (x, y) across the x axis is given as follows;
Coordinates before reflection = (x, y), Coordinates after reflection = (x, -y)
Also, when we rotate a point, (x, y), 90° clockwise, we have;
Image point before 90° clockwise rotation = (x, y), Image point after 90° clockwise rotation = (y, -x)
Therefore, the rotation of the point (x, -y), 90° clockwise will give
Image point before 90° clockwise rotation = (x, -y), Image point after 90° clockwise rotation = (-y, -x)
Which gives the combined transformation as (x, y) → (-y, -x) which is the rule equivalent to reflection about the line y = -x.