Answers
Answer:
s= 14
Step-by-step explanation:
The missing side is s
sin 30° = 7/s switch s and sin 30°
s = 7/sin 30°
sin 30° is 0.5
so :
s = 7/0.5s= 14Related Questions
Triangle ABC is isosceles with AB = AC.
Angle BAC = 110° and the area of the triangle is 85cm^2
Calculate AC.
Answers
Answer:
22.5 cm
Triangle area is (L x W) / 2
7.5 x 6 = 45
45 / 2 = 22.5
Step-by-step explanation:
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The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of days. About what percentage of births would be expected to occur within days of the mean pregnancy length?
About what% of births would be expected to occur within days of the mean pregnancy length.
Answers
Answer: About 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.
Step-by-step explanation:
Complete question is attached below.
Given: The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 8 days.
i.e. [tex]\sigma= 8[/tex]
let X denotes the random variable that represents the lengths of pregnancy.
The probability of births would be expected to occur within 24 days of the mean pregnancy length:
[tex]P(\mu-24<X<\mu+24)=P(\dfrac{\mu-24-\mu}{8}<\dfrac{X-\mu}{\sigma}<\dfrac{\mu+24-\mu}{8})\\\\=P(\dfrac{-24}{8}<Z<\dfrac{24}{8})\ \ \ [\because Z=\dfrac{X-\mu}{\sigma}]\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=P(Z<3)-(1-P(Z<3))\\\\=2P(Z<3)-1[/tex]
[tex]= 2(0.9987)-1\ \ \ [\text{ By z-table}]\\\\=0.9974[/tex]
=99.74%
Hence, about 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.
evaluate arctan(tan(2pi/3))
Answers
Answer:
For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:
[tex] arctan(tan(\frac{2\pi}{3}))[/tex]
Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:
[tex] arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]
Step-by-step explanation:
For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:
[tex] arctan(tan(\frac{2\pi}{3}))[/tex]
Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:
[tex] arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]
Leave the explanation too please.
Answers
Answer:
58 square units.
Step-by-step explanation:
From the graph attached,
Area of the figure = Area of the rectangle A + Area of two squares B and C
Area of rectangle A = Length × width
= 10 × 5
= 50 square units
Area of the square B = (Side)²
= (2)²
= 4 square units
Similarly area of the square C = 2² = 4 square units
Area of the total figure = 50 + 4 + 4
= 58 square units
Therefore, 58 square units will be the answer.
Ejenplo de numeros enteros de una cifra por extension
Answers
Answer:
Un número entero es un número entero que puede ser positivo, negativo o cero. Ejemplos de enteros son: -5, 1, 5, 8, 97 y 3,043. Ejemplos de números que no son enteros son: -1.43, 1 3/4, 3.14,. 09 y 5.643,1.
Translate the scenario below to a linear equation, then solve.
The second angle of a triangle is double the first angle. The third angle is 40 less than the first angle. Find the three angles.
First angle=
Second angle=
Third angle=
Answers
Answer: x + 2x + x-40 = 180
First angle= 55º
Second angle= 110º
Third angle= 15º
Step-by-step explanation: The sum of the angles of a triangle is 180º
Take the values given and use x as the unknown first angle. then create terms for the other two angles based on that:
The second angle of a triangle is double the first angle becomes 2x
The third angle is 40 less than the first angle becomes x-40
x + 2x + x-40 = 180 Solve by adding like terms . x + 2x + x = 4x
4x -40 = 180 Add 40 to both sides to "cancel" the -40 on the left
4x + 40 -40 = 180 + 40 becomes
4x = 220 Divide both sides by 4 to "cancel" the 4 on the left side
4x/4 = 220/4
x = 55 This is the first angle. Substitute 55 for the "x" in the original terms
2(55) = 110 The second angle
(55) -40 = 15 the third angle
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answers
Answer:
fourth option
Step-by-step explanation:
Given
3x³ + 3x² - 18x ← factor out 3x from each term
= 3x(x² + x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, thus
x² + x - 6 = (x + 3)(x - 2) and
3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form
2x -2=10 solve for x
Answers
Answer:
x=6
Step-by-step explanation:
Take -2 and add it to 10 and get 12. So then the equation is 2x=12. Divide 2 by 12 and get x=6.
Ronald bought a car for 2,500. The value of the car depreciates by 6 percent each year. What type of function is this ?
Answers
Answer:
Exponential
Step-by-step explanation:
The liner function represents that there is a constant change in the original value of the asset
While on the other hand the ex[onential function refers to that function in which there is an increase or decreased in the value of the asset that contains the current value of the asset
Hence, the given situation denotes the exponential function
Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle?
Answers
Answer:
9 squares
Step-by-step explanation:
An equilateral has three equal sides. You can have two squares on each side: AB, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC. You can also have two squares on each side - BC, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC. Again, you can have two squares on each side - CA, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC. In addition, AB, BC and CA can be a diagonal of squares.
TL;DR
In conclusion, you have 9 squares in all - 3 as diagonals of squares and 6 as sides of squares. Brainliest appreciated!
No square shares more than two vertices with the equilateral triangle, so we can find the number of squares having two of their vertices at two given points and triple the result. Given 2 points, 3 squares may be drawn having these points as vertices. The figure below shows a red equilateral triangle with the 3 squares that correspond to one of the sides of the triangle. Therefore, 9 squares share two vertices with the equilateral triangle.
Factoriza e indica la cantidad de factores primos: P(m) = a(m+1) + b(m+1) –c(m+1)
A) 2
B) 3
C) 5
D) 1
E) 4
Answers
Answer:
Step-by-step explanation:
P (m) = a (m + 1) + b (m + 1) - c (m + 1)
P (m) = (a + b - c) (m + 1)
There are 2 prime factors
Kellianne lined up the interior angles of the triangle along line p below. Which statements are true for line p? Check all that apply. It is a straight line with a measure of 360°. It stays the same even if the angles in the triangle change. The line will not be straight if one of the angles in the triangle is changed to an obtuse angle. The line is only straight when one of the angles is a right angle. It represents the sum of the measures of the interior angles of the triangle. The line will not be straight if all the angles in the triangle are acute. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.
Answers
Answer:
It stays the same even if the angles in the triangle change. It represents the sum of the measures of the interior angles of the triangle. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.Step-by-step explanation:
The sum of angles in a triangle is always 180°, even if all are acute or one is obtuse or a right angle. That means their sum will always produce a straight line. Thus, the following statements are true
It stays the same even if the angles in the triangle change. It represents the sum of the measures of the interior angles of the triangle. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.Answer:
B,E,G,H
Step-by-step explanation:
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Which phrase describes the algebraic expression 3 x minus 4?
the sum of three times a number and four
four less than three times a number
the quotient of three times a number less four
the difference between four and three
Answers
Answer:
The option B, perfectly gives it to the target, because if you think about it, four less, means 4-, but backwards, and three times, means 3x, and if you put that together, that perfectly matches the one you are looking for. Hope that this would help you!
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
solve it using quadratic formula.
grade 9
10 points
Answers
Answer:
{-1/4, 1}{3/4, 6}Step-by-step explanation:
1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.
[tex]\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}[/tex]
__
2. Using the same idea here, we get ...
[tex]\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}[/tex]
Audrey charges a flat fee of $4 for each delivery plus a certain amount,in dollars per mile, for each mile she drives. For a distance of 30 miles, Curtis and Audrey charge the same amount
Answers
Dyami planted a palm tree in the back yard of his house several years ago. Initially, it was 20 centimeters high and its height increased by 30 centimeters each year. Let H be the height of the tree in centimeters t years after it was planted. Which of the following best explains the relationship between t and H?
Answers
Answer:
when t is increased , h will increased too
Answer:
Th relationship is linear because H increases by 30 each time t increases by 1.
Step-by-step explanation:
H is linear if it changes at a constant rate per unit interval. In other words, constant differences in t should correspond to constant differences in H.
The graph represents this system of equations. A system of equations. y equals 2 x minus 4. y equals 1 minus 3 x. A coordinate grid with 2 lines. The first line passes through (0, 1) and (1, negative 2). The second line passes through (0, 1) and (1, negative 2). What is the solution to the system of equations? (–4, 1) (–2, 1) (1, –4) (1, –2)
Answers
Answer:
(1,-2)
Step-by-step explanation
y = -3x + 1
y = 2x - 4
-3x + 1 = 2x - 4
-5x + 1 = -4
-5x = -5
x = 1
y= 2(1) - 4
y = 2 - 4
y = -2
(1,-2)
Answer:
1/2
Step-by-step explanation:
what does it mean for a savings account to have a minimum balance
Answers
Step-by-step explanation:
You have to retain a certain amount of money
in that account forever. Say you need $50 to
start an account, you have $200 in that account.
You cannot take out more than $150 from that
account.
Answer:
A: If you do not keep at least that much money in the account, you will be assessed fees.
Step-by-step explanation:
combine like terms: 3p2q2-3p2q3+4p2q3-3p2q2+pq PLEASE HELP!!! ASAP!!!
Answers
Answer:
p²q³ + pq and pq(pq² + 1)
Step-by-step explanation:
Given
3p²q² - 3p²q³ +4p²q³ -3p²q² + pq
Required
Collect like terms
We start by rewriting the expression
3p²q² - 3p²q³ +4p²q³ -3p²q² + pq
Collect like terms
3p²q² -3p²q² - 3p²q³ +4p²q³ + pq
Group like terms
(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq
Perform arithmetic operations on like terms
(0) - (-p²q³) + pq
- (-p²q³) + pq
Open bracket
p²q³ + pq
The answer can be further simplified
Factorize p²q³ + pq
pq(pq² + 1)
Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)
What the answer now and answer fast correct answer
Answers
Answer:
[tex] f = 12.7 [/tex]
Step-by-step explanation:
Given:
<H = 94°
FG = h = 15
<F = 58°
GH = f = ?
Use the law of sines to find f:
[tex] \frac{f}{sin(F)} = \frac{h}{sin(H)} [/tex]
[tex] \frac{f}{sin(58)} = \frac{15}{sin(94)} [/tex]
[tex] \frac{f}{0.848} = \frac{15}{0.998} [/tex]
[tex] \frac{f}{0.848} = 15.03 [/tex]
Multiply both sides by 0.848
[tex] \frac{f}{0.848}*0.848 = 15.03*0.848 [/tex]
[tex] f = 15.03*0.848 [/tex]
[tex] f = 12.74544[/tex]
[tex] f = 12.7 [/tex] (nearest tenth)
Set of six numbers has an average of 42. When three of this numbers were removed the remaining three numbers had an average of 72. What was the sum of the removed numbers?
Answers
Answer: 36
Step-by-step explanation:
From the question, we are informed that six numbers has an average of 42. This means that the total number will be equal to:
= 42 × 6
= 252
When three of this numbers were removed the remaining three numbers had an average of 72. The total of this will be:
= 72 × 3
= 216
The sum of the removed numbers will be the difference between the two numbers above. This will be:
= 252 - 216
= 36
Determine whether these two functions are inverses. Show your work please. f(x)=3x+27; g(x)= 1/3x+9
Answers
Answer:
Proved.
Step-by-step explanation:
The functions are:
1.) f(x) = 3x - 27 (* I am giving an answer using this equation. Perhaps you did't copy the question well!)
2.) g(x) = [tex]\frac{1}{3} x[/tex] + 9
If two functions are inverses of each other, then:
f(g(x)) = x and g(f(x)) = x situation must be satisfied.
f(g(x)) = 3([tex]\frac{1}{3}x + 9[/tex]) + 27
We simply it to get;
f(g(x)) = x - 27 + 27 = x (*This is correct)
g(f(x)) = [tex]\frac{1}{3}[/tex](3x - 27) + 9 = x - 9 + 9 = x (* This is also correct!)
In quadrilateral ABCD, angle BAD and angle CDA are trisected as shown. What is the degree measure of angle AFD?
Answers
Explanation:
110 + 100 + 3x + 3y = 360
210 + 3x + 3y = 360
3x + 3y = 150
3(x + y) = 150
x + y = 50
Now look at polygon ABCDF (5 sided polygon)
100 + 110 + x + y + Angle F = 540
210 + 50 + angle F = 540
260 + angle F = 540
Angle F = 280
And:
angle F + AFD = 360 degree
280 + AFD = 360
AFD = 80
Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake. How much space does Lacey's mom cover in frosting?
Answers
Answer:
1360cm²
Step-by-step explanation:
Since the shape of the cake is in L shape, we can divide the cake in to rectangles..
The amount of space covered by the frosting = The sum of the areas of the sides that we can find in this L shaped cake diagram.
The sides of this cake, are shaped like a rectangle.
Hence, Area of a Rectangle = Length × Width
a) Side 1 = Rectangle on the left
Area of a Rectangle = Length × Breadth
Length = 30cm
Breadth =10cm
Area = 30 × 10 = 300cm²
Since we have another side with this measurement/ dimensions also,
Side 2 = 300cm²
Side 3 = The front face of the cube by the right
Area of a Rectangle = Length × Breadth
Length = 22cm - 10cm = 12cm
Breadth =10cm
Area = 12 × 10 = 120cm²
Likewise, we have the another side with the same dimensions as well
Hence, Side 4 = 120cm²
Side 5
30 × 5 = 150cm²
Side 6
10 × 5 = 50cm²
Side 7
20 × 5 = 100cm²
Side 8
22cm × 5 cm = 110cm²
Side 9
10cm × 5cm = 50cm²
Side 10
12cm × 5cm = 60cm²
The amount of space covered by the frosting = Area of Sides( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (300 + 300 + 120 + 120 + 150 + 50 + 100 + 110 + 50 + 60) cm²
= 1360cm²
Answer:
1360
Step-by-step explanation:
it is correct on khan academy
What steps do you use to solve a system of two equations using elimination? For example:
7x +2y = -32
-3x+2y = -70
Answers
Answer:
Step-by-step explanation:
eliminate either vraible, here it is easy to eleimate y, by just subtacting, then solve for x. When you get the value of x, plug in one of the equation and find y. ther you go
Answer:
x= 3.8
y= -29.3
Step-by-step explanation:
Which of the following is a like radical to 3x sqrt 5
Answers
Answer:
The last option
Step-by-step explanation:
Source: Trust bro
Answer:
d) y sqrt 5
Step-by-step explanation:
radicals are like if they have the same index and radicand, here they are both square roots and have a radicand of five
Find arc length. (Ignore the pencil mark, NEED ASAP)
Answers
Answer:
15.7 yd
Step-by-step explanation:
Arc length is given as 2πr(θ/360).
Where,
Radius (r) = 10 yd,
Measure of arc (θ) = 90°
π = 3.142
Arc length = 2*3.142*10(90/360)
Arc length = 62.84(¼)
Arc length = 62.84/4
Arc length = 15.71 yd
The act length is approximately 15.7 (to the nearest tenth)
please help :) Which number is less than 2.167 × 10 to the 4 power? A. 9,978 B. 1.1 x 10 to the 6 power C. 56,344,000 D. 2.468 × 10 to the 5 power
Answers
Answer: A
Step-by-step explanation
2.167x10^4 = 21,670
= 9,978
1.1x10^6 = 1100,000
= 56,344,000
2.468x10^5 = 246,800
Answer: A. 9,978
Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)
2.167 × 10^4 = 21670
1.1 × 10^6 = 1100000
2.468 × 10^5 = 246800
Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.
Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bottom face included), what is the surface area of the roof of the kennel, including the bottom face?
Answers
Answer:
Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2
Step-by-step explanation:
The image is attached below
For the triangular sides of the roof, area is
A = [tex]\frac{1}{2}bh[/tex]
where b is the base = 4 ft
h is the vertical height = 2.24 ft
A = [tex]\frac{1}{2}*4*2.24 =[/tex] 4.48 ft^2
for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2
For the rectangular sections of the roof, area is
A = [tex]lh[/tex]
where [tex]l[/tex] is the length of the rectangle = 5 ft
h is the height of the rectangle = 3 ft
A = 5 x 3 = 15 ft^2
For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2
For the bottom face, area is
A = [tex]lw[/tex]
where [tex]l[/tex] is the length of the house = 5 ft
w is the width of the house = 4 ft
A = 5 x 4 = 20 ft^2
Surface area of the roof of the dog kennel is
8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2
HELP ASAP!
The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals?
Answers
Answer:
My conclusion about Quadrilaterals ABCD and EFCD is that both quadrilaterals are similar to each other.
THE REASON IS BECAUSE THE SIDES OF QUADRILATERAL ABCD ARE THE SAME AS THE SIDES OF QUADRILATERAL EFCD.
Step-by-step explanation:
When we are given vertices, (x1, y1) , (x2 ,y2), we use the formula:
√(x2 - x1)² + (y2 - y1)²
For quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)
Side AB: A(4, 8), B(10, 10)
√(x2 - x1)² + (y2 - y1)²
√(10 - 4)² + (10 - 8)²
= √6² + 2²
= √40
Side BC: B(10, 10), C(10, 4)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 10)² + ( 4 - 10)²
= √ 0² + (-6)²
= √36
= 6
Side CD: C(10, 4), D(4, 4)
√(x2 - x1)² + (y2 - y1)²
= √ (4 - 10)² + ( 4 - 4)²
= √-6² + 0²
= √36
= 6
Side AD: A(4, 8), D(4, 4)
=√(x2 - x1)² + (y2 - y1)²
= √(4 - 4)² + (4 - 8)²
= √0² + (-4²)
= √16
= 4
Therefore, for Quadrilateral ABCD
Side AB = √40
Side BC = 6
Side CD = 6
Side AD = 4
For quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).
Side EF: E(4, 0), F(10, -2)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 4)² + (-2 - 0)²
= √6² + 2²
= √40
Side FC: F(10, -2), C(10, 4)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 10)² + (4 -(-2))²
= √ 0² + 6²
= √36
= 6
Side CD: C(10, 4), D(4, 4)
√(x2 - x1)² + (y2 - y1)²
= √(10 - 4)² + (4 - 4)²
= √6² + 0²
= √36
= 6
Side ED: E(4, 0), D(4, 4)
√(x2 - x1)² + (y2 - y1)²
= √(4 - 4)² + (4 - 0)²
= √0² + 4²
= √16
= 4
Therefore, for Quadrilateral EFCD
Side EF = √40
Side FC = 6
Side CD = 6
Side ED = 4
My conclusion about Quadrilaterals ABCD and EFCD is that both quadrilaterals are similar to each other.
THE REASON IS BECAUSE THE SIDES OF QUADRILATERAL ABCD ARE THE SAME AS THE SIDES OF QUADRILATERAL EFCD.