Length of CA = 6x - 30
Length of AT = 2x + 30
We know that all sides of a rhombus are congruent.
Which means :
[tex] = 6x - 30 = 2x + 30[/tex]
[tex] = 6x - 30 - 2x = 30[/tex]
[tex] = 4x - 30 = 30[/tex]
[tex] = 4x = 30 + 30[/tex]
[tex] = 4x = 60[/tex]
[tex] = x = \frac{60}{4} [/tex]
[tex] = x = 15[/tex]
Thus, the value of x = 15
Then :
Measure of CA :
[tex] = 6x - 30[/tex]
[tex] = 6 \times 15 - 30[/tex]
[tex] = 90 - 30[/tex]
[tex] = 60[/tex]
Thus, measure of CA = 60
Measure of AT :
[tex] = 2x + 30[/tex]
[tex] = 2 \times 15 + 30[/tex]
[tex] = 30 + 30[/tex]
[tex] = 60[/tex]
Thus, measure of AT = 60
Perimefer of rhombus CAT :
[tex] = 4 \times side[/tex]
[tex] = 4 \times 60[/tex]
[tex] = \color{plum}240[/tex]
Therefore, the perimeter of rhombus CAT = 240
Plz help this one is the last one of the day plz help
The pointer on a voltmeter is 6 in length. Find the number of degrees through which the pointer rotates when it moves 2.1 centimeters on the scale.
Anyone know?
Answer:
The number of degrees through which the pointer rotates is approximately 20°.
Step-by-step explanation:
If the pointer moves, then it is moving in form of an arc. Since the length of the pointer is 6cm, then radius formed with the pointer is 6cm in length.
When it moves 2.1cm on the scale, an arc with length of 2.1cm is formed.
Using the formula for the length of an arc, we can get the desired number of degrees, angle in degrees, needed.
Length of an arc = 2πrA/360°
Length of the arc = 2.1cm
r = 6cm
A = the angle in degrees.
Therefore we have:
2.1 = 2xπx6xA/360
2.1 = πA/30
(2.1x30)/π = A
A ≈ 20°
The number of degrees through which the pointer rotates when it moves 2.1 centimeters on the scale is; 20°
When the pointer moves 2.1 centimetres on the voltmeter scale;
This means that the length of the arc formed is; 2.1 cm.In essence, since the length of an arc is given by;
L(arc) = (p/360) × 2 × π × Rwhere, R = radius = 6cm
p = angle subtended = ?π = 3.142.Therefore;
2.1 = (p/360) × 2 × 3.142 × 6p = (360×2.1)/(2×3.142×6)p = 20°.
Read more on length of an arc;
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Dennis can walk about 2 5/6 miles each hour. About how far can he walk in 3 hours 15 minutes?
Answer:
24 13/34
Step-by-step explanation:
The distance covered by Dennis will be 9.23 miles.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity and does not require any direction to represent it.
Given that Dennis can walk about 2(5/6) miles each hour. The distance covered by Dennis in 3 hours 15 minutes will be calculated as:-
Distance = 2 ( 5 / 6) x 3 hour 15 minute
Distance = 2.84 x 3 ( 1 / 4)
Distance = 2.84 x 3.25
Distance = 9.23 miles.
Therefore, the distance covered by Dennis will be 9.23 miles.
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Teegan accidentally ran over a nail while driving to school today. Air is leaking out of her tire at a rate of 3 psi (pounds per square inch) per day. If her tire has 36 psi now, which sequence represents the psi remaining in Teegan's tire for the next four days?
{0, 3, 6, 9, …}
{36, 33, 30, 27, …}
{36, 12, 4, 0.75}
{36, 33, 30, 27}
The sequence will be {36, 33, 30, 27, ....}. Then the correct option is B.
What is the arithmetic sequence?Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as
[tex]\rm a_n = a_1 + (n - 1)d[/tex]
Teegan accidentally ran over a nail while driving to school today.
Air is leaking out of her tire at a rate of 3 psi (pounds per square inch) per day.
If her tire has 36 psi now.
Then we have
a₁ = 36
d = -3
Then the sequence will be
The second term will be
a₂ = 36 + (2 – 1)-3
a₂ = 33
The third term will be
a₃ = 36 + (3 – 1)-3
a₃ = 30
The fourth term will be
a₄ = 36 + (4 – 1)-3
a₄ = 27
Then the sequence will be {36, 33, 30, 27, ....}.
Then the correct option is B.
More about the arithmetic sequence link is given below.
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Answer:
{36, 33, 30, 27}
Step-by-step explanation:
It only asks for the next four days, not indefinitely.
What is 32, 749 rounded to the nearest hundred?
Answer:
32,800
Step-by-step explanation:
A dollar bill is about 0.00011 meter thick. What is this thickness in scientific notation?
Answer:
1.1×10^-4
Step-by-step explanation:
we move the point from where to in between 1.1 and counts the number of numbers it has crossed..in this case it 4...which should be -4
if the angles of a triangle are 45°, 45°, and 90° show that the length of the hypotenues is √2 times as long as each leg
Answer:
Step-by-step explanation:
2
(a )square root of 2 (c)
Answer:
Step-by-step explanation:
Use the drop-down menus to complete each equation so the statement about its solution is true.
Answer:
See below
Step-by-step explanation:
Equation given
2x + 9 + 3x + x = 6x + 9No solution ⇒ 6x + a, a≠9
Parallel lines, same slope and different y-interceptOne solution ⇒ ax + b, a≠6
Lines with different slopeInfinitely many solutions ⇒ a(6x + 9), a≠ 0
Overlapping linesA pigeon leaves its nest in New York City and
flies 5 km due east. The pigeon then flies 3 km
due north. How far is the pigeon from its nest?
PLEASEEEE ANSWERR FASTTT
The distance of the pigeon from the nest is 5.8 km.
In order to determine the distance of the pigeon from its nest, the Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where:
a = length b = base c = hypotenuse3² + 5²
= 9 + 25
= 34
√34 = 5.8 km.
To learn more about Pythagoras theorem, please check: brainly.com/question/20936855?referrer=searchResults
What is the tangent ratio for
• 4/3
• 5/4
• 5/3
• 3/4
Answer:
Try the answer 5/3
or in other words C.
Using the graph above, identify the constant of proportionality between the number of shirts and how much they cost? Hint: simplify your answer
A. K=80
B. K=20
C. K=10
D. K=8
what is the percent rate of change in function y = (0.98) ^ x? determine whether the function represents exponential growth or exponential decay
C. 2%; exponential decay
You can use the fact that increasing power of values lying between 0 and 1 results in less and less values.
The percent rate of change in given function is -2%
The function represents exponential decay.
Given that:The function: [tex] y = (0.98) ^ x[/tex]To find:Percent rate of change in given function.Is it representing exponential growth or exponential decay?Finding percent rate of change in given function:
For finding this, first find how much the output y changes if we change x from x to x + 1.
Output when x = x: [tex]y = (0.98)^x[/tex]
Output when x = x+1: [tex]y = (0.98)^{x+1}[/tex]
Difference in output if x goes from x to x+1: [tex](0.98)^{x+1} - (0.98)^x = (0.98)^x(0.98 - 1) = -0.02 \times (0.98)^x[/tex] (this change occurs if we increase input x by 1 unit, thus this also represents the rate)
Rate of change of function per unit increment = [tex]-0.02 \times (0.98)^x[/tex]
The percentage of rate of change is found as:
[tex]\text{Percent rate of change\:} = \dfrac{\text{Rate of change} \times 100}{\text{previous value}} = \dfrac{-0.02 \times (0.98)^x \times 100}{(0.98)^x} \\\\ \text{Percent rate of change\:} = -2\%[/tex]
Thus, the percent rate of change is -2%
The negative sign shows that the value is decreasing, thus showing that function shows exponential decay.
Learn more about exponential growth or decay here:
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Find the x and y intercepts of the equation: 5x−7y=−105
Answer:
X intercepts: (21,0)
Y intercepts: (0, -15)
Step-by-step explanation:
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
Please help its a emgrency its a test
Ethan can find the distance between two cities using the map scale in which 2 centimeters represents 15 miles. The distance between Mesquite and Terrell is 5 centimeters on the map. What is the actual distance between these two cities in miles?
Answer: 4 centimeters is 30 and then you would have to find half of 15 I'm pretty sure that's 7.5. Is there an answer that says: 37.5?
Answer:
37.50
Step-by-step explanation:
i think sorry if im wrong
How many 1/3 inch cubes does it take to fill a box with width 2 2/3 inches, lengths 3 1/3 inches, and height 2 1/3 inches?
Answer:
560 cubes
Step-by-step explanation:
width: 8 cubes
length: 10 cubes
height: 7 cubes
volume: 8*10*7=560
divided l, w, and h by 1/3 to get them in cubes
Answer:
Step-by-step explanation:
The awnser is multiply by 9 then multiply by 2
Tell me the coordinates to graph it plz
Answer:
x=2, y=3
Step-by-step explanation:
Change 0.3 into a fraction
Answer:
3/10
Step-by-step explanation:
0.3 is 3 divided by 10, or 3/10
Pls helppppppppp :((((((((((((
Answer:
The answer is C
What is the center and radius of circle with the equation? x^2+ y^2+12x-8y+39 = 0
Answer:
Center is (-6,4) and the radius is √13
Step-by-step explanation:
A rectangular gate is made using 6 straight pieces of steel.
5 m
12 m
The weight of the steel is 2.5 kg per metre.
+
Work out the total weight of the steel gate.
Pythagoras' Theorem - A Simple Approach View One Minute Version
Overview
11.
معاص
Answer:
Total weight is 150 kg
Step-by-step explanation:
Firstly, we need the weight of the diagonal
To get this, we shall use the Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
The diagonals stand for the hypotenuse
Thus, we have that;
d^2 = 5^2 + 12^2
d^2 = 25 + 144
d^2 = 169
d^2 = 13^2
d = 13
The 6 sides technically includes the whole rectangle sides, then the two diagonals
The total length here is;
2(5 + 12 + 13) = 60 meters
Steel weight is 2.5 kg per meter
Weight of 60 m will be ;
60 * 2.5 = 150 kg
plz help ! 15 points
Factor each trinomial completely 4x2 – 25b2
Answer:
(2x + 5b) • (2x - 5b)
Step-by-step explanation:
or at least that's what I got
What is the value of (x)?
Answer:
1
Step-by-step explanation:
Answer:
x=1
Step-by-step explanation:
Last question on homework I’m having trouble with ^_^
Answer:
25 + h
f^2
Step-by-step explanation:
It says the sum of 25 and h which is 25 + h.
Now, it basically says "25 + h" is divided by f cubed. Cubed means to the power of 2 (the exponent), so f cubed would be f^2 (f to the power of 2).
25 + h is divided by f^2
25 + h
f^2
(the reason I put "^2" is because I don't know how to put exponents on here, sorry)
Find the length of the line d pictured below
Use the pythagreon theorem
Answer:
d = 19
Step-by-step explanation:
________________________________
FACTS TO KNOW BEFORE SOLVING :-
For a cuboid with dimensions l , b & h ,
Diagonal of a cuboid = [tex]\sqrt{l^{2} + b^{2} + h^{2}}[/tex]
________________________________
According to the question ,
l = 10 ; b = 6 ; h = 15
So , Diagonal of the cuboid (d) =
[tex]d = \sqrt{10^{2} + 6^{2} + 15^{2}} = \sqrt{100 + 36 + 225} = \sqrt{361} = 19[/tex]
HELP QUICKEST GETS BRAINLIEST PLZZ FOR NTH TERM
Answer:
The nth term of this sequence is T = n^2 + 2n + 1
the general term is Tn = n^2 + 2n + 1
What is the solution to 0.4(12-3x)=0.3(12x-16)
Step 1: Simplify both sides of the equation.
0.4(12−3x)=0.3(12x−16)
(0.4)(12)+(0.4)(−3x)=(0.3)(12x)+(0.3)(−16)(Distribute)
4.8+−1.2x=3.6x+−4.8
−1.2x+4.8=3.6x−4.8
Step 2: Subtract 3.6x from both sides.
−1.2x+4.8−3.6x=3.6x−4.8−3.6x
−4.8x+4.8=−4.8
Step 3: Subtract 4.8 from both sides.
−4.8x+4.8−4.8=−4.8−4.8
−4.8x=−9.6
Step 4: Divide both sides by -4.8.
−4.8x /−4.8 = −9.6 /−4.8
x = 2
11. Rebecca is building a pen for her rabbits against the side of her house.
The polynomial 4n+ 8 represents the length and the polynomial 2n = 6
represents the width
2n +6
What polynomial represents the perimeter
of the entire pen?
a
4n+8
m и с от
b. What polynomial represents the perimeter
of the pen NOT including the side of the house.
Ok
Answer:
a. 12n + 28
b. 8n + 20
PLZZZZ HELP Write 512 as a product of primes use index notation
Answer:
[tex]\mathbf{512 = 2 \times 2 \times 2\times 2\times 2\times 2\times 2\times 2\times 2}[/tex]
Step-by-step explanation:
Prime numbers are those numbers in which they can be divided by itself and 1. They are formed by two natural numbers higher than 1 but not by multiplying natural numbers that are smaller.
So; using index notation to writing 512 as a product of primes; we have:
[tex]\mathbf{512 = 2 \times 2 \times 2\times 2\times 2\times 2\times 2\times 2\times 2}[/tex]
An ice cream shop is choosing a milk delivery service. The Spotted Cow charges $2.80 per gallon, plus a $2 delivery fee. Dairy Farms charges $2.10 per gallon, plus a $10 delivery fee. If the ice cream shop uses 20 gallons a milk per week, which service is a better deal? Group of answer choices
Answer:
The Dairy Farm is better deal.
Step-by-step explanation:
Given that:
Per gallon charges of the Spotted Cow = $2.80
Delivery fee = $2
Let,
x be the gallons of milk.
S(x) = 2.80x + 2
Putting x = 20
S(20) = 2.80(20) + 2 = 56 + 2
S(20) = $58
Per gallon charges of the Dairy Farms = $2.10
Delivery fee = $10
D(x) = 2.10x + 10
Putting x = 20
D(20) = 2.10(20) + 10 = 42 + 10
D(20) = $52
Hence,
The Dairy Farm is better deal.
Solving For X With Fractions, Pls Help, Will Give Brainliest