Answer:
Step-by-step explanation:
Use the Pythagorean Theorem
diagonal² = 16² + 12² = 400
diagonal = √400 = 20 cm
53. A right triangle has a hypotenuse measuring 15 inches and one leg measuring 9 inches What is the length, in inches, of the other leg of the triangle?
A. 3
B.6
C. 10
D. 12
Answer:
D
Step-by-step explanation:
Pythagorean
[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)
=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]
Find the equation of the line formed made by joining the pints (-2,-4),(-8,10)
Answer:
y = (-7/3)x - 26/3
Step-by-step explanation:
To find the equation of a line given two points, we can first define an equation of a line to be y= mx +b, with m being the slope and b being the y intercept.
To calculate the slope, we can use the formula (change in y)/(change in x), or
(y₂-y₁)/(x₂-x₁). If we define (-2, -4) as point 1 (meaning -2 is x₁ and -4 is y₁) and (-8, 10) as point 2 (it doesn't matter which point is point 1/2), we can say that the slope is equal to
(10-(-4)) / (-8-(-2)
= 14/(-6)
= -7/3
Therefore, our formula so far is
y = (-7/3)x + b
To figure out b, we can plug in a point, e.g. (-8, 10) and solve for b. Plugging this in, we get
10 = (-7/3)(-8) + b
10 = 56/3 + b
subtract 56/3 from both sides
10 - 56/3 = b
= 30/3 - 56/3
= -26/3
Therefore, our equation is
y = (-7/3)x - 26/3
What is the function of this
Answer:
f(x) = x⁴ + 2x³ - 3x² - 4x + 4
Step-by-step explanation:
we have 3 turnarounds and no negative y values (so, it should be a function based on x⁴), 2 of these turnarounds are also directly on the x-axis (y=0).
f(0) = 4
f(1) = 0
f(-2) = 0
an equation based on x⁴ would have 4 interceptions with the x-axis. since we have only 2 here, then there must be 2 pairs of equal interceptions.
based on the known x-interceptions (x=1, x=-2) we can start with the approach
(x-1)(x+2)
this world give us a quadratic equation (based on x²).
the trick is now to get this to x⁴ without adding additional x-interceptions. that is done by simply "reusing" the ones we already used.
(x-1)(x+2)(x-1)(x+2) = (x-1)²(x+2)²
(x-1)²(x+2)² = (x² - 2x + 1)(x² + 4x + 4) =
x⁴ - 2x³ + x² + 4x³ - 8x² + 4x + 4x² - 8x + 4 =
x⁴ + 2x³ - 3x² - 4x + 4
Help me solve this problem please
Answer:
A is ur answer
Step-by-step explanation:
Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 8 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
Answer:
Step-by-step explanation:
If we are looking for how long it will take the level to be less than or equal to 64 cups, we are solving an inequality as opposed to an equation. It would look like this:
-.414t + 129.549 ≤ 64 We subtract 129.549 from both sides to get
-.414t ≤ -65.549 and then divide by -.414. But because we are dividing by a negative number we need to change the way the inequality is pointing:
t ≥ 158.3 minutes which is about 2.6 hours
Answer:
t ≥ 158.33, or rounded, t ≥ 160.
Explanation:
The equation we're given is
W = -0.414t + 129.549, which an be written as
-0.414t + 129.549 = W.
We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups. Plugging this information in, we have:
-0.414t + 129.549 ≤ 64
To solve this, we first cancel 129.549 by subtracting from both sides:
-0.414t + 129.549 - 129.549 ≤ 64 - 129.549
-0.414t ≤ -65.549
Now divide both sides by -0.414:
-0.414t/-0.414 ≤ -65.549/-0.414
t ≥ 158.33
(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol)
PLS HELP!!! The problem is in the photo attached
Answer:
The answer is C!
Step-by-step explanation:
Answer:
D
NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"
Step-by-step explanation:
if triangle 3 shows a 100 degree rotation of triangle 1 about point p what is the degree of intersection of lines m and n?
The given transformations are rigid transformations, such that
the image and the preimage have the same dimensions.
Correct responses:
The degree of the intersection of lines m and n is; 50°This image also shows two A. reflection about lines m and then line n. How can the angle between the lines be determined, and what is a reflection?Given;
The images of triangle 1 are; Triangle 2, and triangle 3
Taking the image of line m as line m, we have;
Required:
The degree of the intersection of lines m and n
Solution:
Triangle 2 is the reflection of triangle 1 across line m, and
triangle 3 is the reflection of triangle 2 across line n
The distance of triangles 1 and 2 from line m are equal
The distance of triangle 2 and 3 from line n are equal.
Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is
equal to the degree of rotation of triangle 2 to triangle 3, θ₂,
we have;
θ₁ = θ₂
100° = θ₁ + θ₂ = 2·θ₁
θ₁ = θ₂ = 100° ÷ 2 = 50°
The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°
The degree of the intersection of lines m and n = 50°The transformation to give triangle 2 from triangle 1 is a reflection about line m.
Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.
Therefore;
The image also shows two A. Reflections about line m and then line n.Learn more about rigid transformations here:
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Can someone help me with this math homework please!
Answer:
X1 = 2 Y1 = -5
Step-by-step explanation:
math simple slope
Solve for x. 4/3 = 24/x
Help me please!!
Thank you so much thank y’all
Answer:
x > 20
Step-by-step explanation:
5x + 20 > 120
Divide 5 on both sides,
x + 4 > 24
x + 4 - 4 > 24 - 4
x > 20
Find the center and radius of the circle with the equation x^2 + y^2 = 9. Then graph the circle.
Answer:
center = origin (0,0)
radius = 3
to graph it, draw a circle that goes through the points (3,0), (0,3), (-3,0), (0,-3)
Step-by-step explanation:
Help please
Find the volume of this cone.
Use 3 for T.
V
Tr²h
3
V =
V ~ [?]cm3
112cm
8cm
Answer:
192
Step-by-step explanation:
3(pi) x 4^2 x 12 ÷ 3 = 192
i need help plz!!!!!!!!!!!!
Answer:
54 and 36
Step-by-step explanation:
84
45% of 120 students chose the amusement park , then
45% of 120 = 0.45 × 120 = 54
54 students chose the amusement park
85
45% of 180 = 0.45 × 180 = 81
25% of 180 = 0.25 × 180 = 45
81 - 45 = 36
36 more students chose the amusement park than the water park
Answer:
54, 36
Step-by-step explanation:
84
45% of 120 students chose the amusement park
45% of 120 = 0.45×120=54
54 students chose the amusement park
85
45% of 180 = 0.45 × 180 = 81
25% of 180 = 0.25 × 180 = 45
81 - 45 = 36
36 students chose the amusement park than the water park
what is the answer to this? help, please
This is because angles 1 and 4 are vertical angles. Such angles form whenever we have an X shape like this. Vertical angles are always opposite one another and they are always the same measure. The fact that lines k and l are parallel has no relevance (so they could easily be not parallel and the two angles mentioned are still congruent).
Simplify as far as possible
Please help
x²+3x²-4x²+5x
Answer:
I think 5x is the answer
stay safe
An automobile manufacturing plant produced vehicles today: were sedans, were trucks, and were motorcycles. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. What is the probability that two motorcycles will be selected
Answer:
120 / 561
Step-by-step explanation:
An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected
16/34 X 15 X 33
| 2. You are given an isosceles trapezoid ABCD with median XY. Complete the following.
m
Answer:
m∠CDA=65°
Step-by-step explanation:
This is because an isosceles trapezoid has both pairs of base angles that are equivalent to one another.
Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.
Answer:
sin θ = (√119)/12
tan θ = (√119)/5
csc θ = 12/(√119)
cot θ = 5/(√119)
Five trigonometric functions of θ are
sinθ = [tex]\frac{\sqrt{119} }{12}[/tex]cosθ = [tex]\frac{5}{12}[/tex]tanθ = [tex]\frac{\sqrt{119} }{5}[/tex]cosecθ = [tex]\frac{12}{\sqrt{119} }[/tex]secθ = [tex]\frac{12}{5}[/tex]cotθ = [tex]\frac{5}{\sqrt{119} }[/tex]
What is trigonometric functions?"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."
Let θ be an acute angle of a right angle triangle
What is acute angle?"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."
What is right angled triangle?"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).
What is hypotenuse?"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."
What is opposite side?"An 'opposite' side is the one across from a given angle."
What is adjacent side?"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."
we have,
cosθ = [tex]\frac{5}{12}[/tex]
secθ = [tex]\frac{12}{5}[/tex]
Hypotenuse side = 12
Adjacent side = 5
∴ Opposite side = [tex]\sqrt{hyp^{2}-adj^{2} }[/tex]= [tex]\sqrt{12^{2}-5^{2} }[/tex] = [tex]\sqrt{119}[/tex]
sinθ = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]
tanθ = [tex]\frac{opp}{adj}[/tex] = [tex]\frac{\sqrt{119} }{5}[/tex]
cosecθ = [tex]\frac{hyp}{opp}[/tex] = [tex]\frac{12}{\sqrt{119} }[/tex]
cotθ = [tex]\frac{adj}{opp}[/tex] = [tex]\frac{5}{\sqrt{119} }[/tex]
Learn more about trigonometric functions, acute angle and right angle triangle here
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Now measure the lengths of the sides of polygon ABCD and tbe lengths of the sides of the translated images. Record the measurements in the table.
Answer:
3.16, 3.16, 3.16
3.16, 3.16, 3.16
1.41, 1.41, 1.41
3.16, 3.16, 3.16
Step-by-step explanation:
Answer:
Length Length Length
3.16 3.16 3.16
3.16 3.16 3.16
1.41 1.41 1.41
3.16 3.16 3.16
Step-by-step explanation:
The iPod costs $200.00. If Alex did his jobs every week, then how long would it take him to earn $200.00??
Plz help I’m confused
Answer:
It would take him 5.9 weeks (rounded). basically almost 6 weeks
Step-by-step explanation:
he makes 6 dollars a week by walking the dog out. he earns 2$ every time he walks the dog out, and he does it 3 times, so 2 x 3 = 6
he makes another 10 dollars a week by babysitting. he earns 2.50$ per hour of babysitting, and he does it for 4 hours per week, so 2.50 x 4 = 10
he makes another 18$ dollars a week by mowing the lawn. he does this once a week. he gets 15$ dollars if he mows, and another 3$ if he pulls weeds. if he does both, he would get 15+3 = 18$ per week by mowing
so add the numbers 6, 10, and 18, and you get 34.
he makes 34 dollars a week
divide the number he wants to make by what he earns in a week to figure out how many weeks it would take.
he wants to get 200$, so the equation is
200 / 34 = 5.88
Its 5.9 rounded or 5.88 weeks exact.
Answer:
6 weeks
Step-by-step explanation:
Job 1:
2 x 3 = 6
$6 per week
Job 2:
2.50 x 4 = 10
$10 per week
Job 3:
15 + 3 = 18
$18 per week
6 + 10 + 18 = 34
$34 per week
200/34 = 5.88
answer is needed however explanation is needed more..
no. of even factora of 120 which are greater than 20 and less than 120 are = 6
6a²+11x-10= answer.
6a²+11x-10= (3a+5)(3a-2)
Answer:
Solution given:
6a²+11x-10
doing middle term factorisation
6a²+(15-4)x-10
6a²+15x-4x-10
3a(3a+5)-2(3a+5)
(3a+5)(3a-2)
Step-by-step explanation:
if
6a²+11x-10=0
(3a+5)(3a-2)=0
either
a=-5/3
it
a=⅔
A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this spinner 1000 times, how many times do you expect it to land on Red?
Answer:
83 spins
Step-by-step explanation:
Number of red spins = n
Number of orange spins = 8n
Number of yellow spins = 3n
Total number of trials = 240
Total number of spins :
(n + 8n + 3n) = 240
12n = 240
n = 240 / 12
n = 20
Number of red spins = 20
(1000/240) * n
4.1666666 * 20
= 83.333
= 83 spins
Which are the solutions of x2 = -7x – 8?
Ž
17 7
4
+
17
4
-
글
그를
+
ZIA
+
V 17
4
4
7 - 17 7 + /17
-
-7 - V 17 -7 + v17 .
2
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
please help me with this fast please
Answer:
the last one
Step-by-step explanation:
What is the product of `4` and `-2x + 3`?
9514 1404 393
Answer:
-8x +12
Step-by-step explanation:
The distributive property can help you simplify the product.
(4)(-2x +3) = (4)(-2x) +(4)(3) = -8x +12
On a unit circle, the terminal point of 0 is (1/2, square root of 3/2) what is 0
Answer: pi/6
explanation: took test
The value of θ on a unit circle where the terminal point of θ is (1/2,square root 3/2), is 60°.
Terminal PointThe measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane is known as terminal point
How to solve this problem?Given On a unit circle, the terminal point of θ is [tex](\frac{1}{2},\frac{\sqrt{3} }{2} )[/tex]According to image below the value of θ at terminal point (1/2,square root 3/2) is 60 degrees.Thus the value of θ at terminal point on a unit circle (1/2,square root 3/2) is 60 degrees.
Learn more about Terminal Point here:
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a plane traveled 510 miles in 1.5 hours. What was the average rate of speed of plane?
Answer:
340 miles per hour
Step-by-step explanation:
To find the speed, take the distance and divide by the time
510 miles / 1.5 hours
340 miles per hour
Answer:
340 miles
Step-by-step explanation:
Speed= Distance/ Time=
510/ 1.5= 340 miles
Find the value of x in the isosceles triangle shown below.
2
2
5
8
Answer:
[tex]\sqrt{41}[/tex]
Step-by-step explanation:
think of this triangle being made up of 2 triangles with the lengths of 5, 4, and x.
x being the hypotenuse, 5 being one of the legs, and 4 being one of the legs. (8/2).
pythagorean theorem:
a^2 + b^2 = c^2
5^2 + 4^2 = x^2
25 + 16 = x^2
41 = x^2
x = sqrt 41
Please help me I have been stuck on this question forever
19 Step-by-step explanation:
Answer:
3.45 sqft
Step-by-step explanation:
Calculate all the areas individually, the 3 lateral sides are the same and using the formula for area we have 1/2 base times height. The height is 2 ft and the base is 1 ft so the area of one of the lateral sides is 1 ft.
There are three lateral sides so you multiply 1 by 3 to get 3.
The base is done the same way. It's base is 1 ft and it's height is 0.9ft so the area is 0.45.
3 + 0.45 = 3.45
The surface area is 3.45 sqft.
I could be wrong but the formula and process is the same, calculate the sides individually using the base height formula for area.
