the answer is 22 degrees
The area covered by the blade as it rotates through an angle of 122 degrees is approximately 346 square inches.
We have,
The area of a sector can be calculated using the formula:
Area = (θ/360) * π * r²
where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sector.
The central angle is 122 degrees, and the radius of the wiper blade is 18 inches.
Substituting the values into the formula:
Area = (122/360) * π * (18²)
Area = (0.3389) * 3.14159 * 324
Area ≈ 344.77 square inches
Area = 345 square inches
Therefore,
The area covered by the blade as it rotates through an angle of 122 degrees is approximately 346 square inches.
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what are the soultions of 3(x-4) (2x-3)= 0 check all
Answer:
{3/2, 4}
Step-by-step explanation:
Set x - 4 = 0 and solve for x: x = 4 is a solution.
Seet 2x - 3 = 0 and solve for x: 3/2 is another solution.
Which expression represents a difference of squares ?
Answer:
first and last options
Step-by-step explanation:
Difference of squares are in the form a² - b². The only choices that satisfy this are 25x² - 36 and 1 - 16x².
Answer:
1 and 4
Step-by-step explanation:
What is the Square root of -100
Answer:
[tex]10i[/tex]
Step-by-step explanation:
√(-100)
Use the imaginary number rule [tex]i=\sqrt{-1}[/tex]
√(-1) × √(100)
i × √(10²)
i × 10
= 10i
Answer:
It does not have a square root because it is a minus digit.
Step-by-step explanation:
The square root of one number is the number which is multiplied by itself to form the square number.
But, no negative number has a square root, because
- x - = +
+ x + = +
As you can see, no two same signs multiply together to form a negative.
Hope this helps.
Good Luck
If h(x) = 5 + x and f(x) = 5, which expression is equivalent to (kn)(x)?
Answer:
Step-by-step explanation:
The question is not correctly written, here is the correct question.
If h(x) = 5 + x and k(x) = 5, which expression is equivalent to (koh)(x)?
(koh)(x) can be rewritten as k{h(x)}
Since h(x) = 5+x then, k{h(x)} = k(5+x)
Note that k(x) can be written as 5x°
k(5+x) = 5(5+x)°
Since any value raise to the power of zero is 1, then;
k(5+x) = 5(1)
k(5+x) = 5
(koh)(x) = k{h(x)} = 5
For (hok)x;
(hok)x = h{k(x)}
= h(5)
= h(5x°)
Since h(x) = 5+x
h(5x°) = 5+5x°
h(5x°)= 5+5 = 10
(hok)x = h(k(x)) = 10
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JL=25 and JM=5, find KM.
HELP ME PLEASE!!!!!!
Answer:
KM = 15
Step-by-step explanation:
From the diagram, ΔJKL and ΔJKM are similar to each other because they share the same angle J and they are both right angle triangle. Therefore they are similar by AA property.
Since JL=25 and JM=5, JM = JL + JM= 25 + 5 = 30
Since ΔJKL and ΔJKM are similar to each other, therefore:
[tex]\frac{JK}{JL}=\frac{JM}{JK}\\ Substituting:\\\frac{JK}{30}=\frac{5}{JK}\\JK^2=150\\JK=\sqrt{150}\\ \\From\ hypotenuse:\\JK^2=JM^2+KM^2\\Substituting:\\(\sqrt{150} )^2=5^2+KM^2\\150=25+KM^2\\KM^2=150-25=125\\KM=\sqrt{125}\\ KM=15[/tex]
Melanie began studying a sample of the chemical element einsteinium-253 which naturally loses its mass over time. The relationship between the elapsed time, t, in days, since Melanie started studying the sample, and the total mass remaining in the sample, M(t), in micrograms, is modeled by the following function: M(t)=169⋅(0.96)^t. How much percent does the chemical element lose weight by everyday?
Answer:
The chemical element loses 4% of its weight everyday
Step-by-step explanation:
Here, we are interested in knowing the percentage weight loss of the chemical each day.
The key to answering this is looking at the expression inside the bracket.
We can express M(t) = 169•(0.96)^t as
M(t) = 169•(1-0.04)^t
So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here
Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%
Answer:
0.96
Step-by-step explanation:
The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.
The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.
Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.
PLEASE HELP!!!! BRAINLIEST FOR RIGHT ANWSER
Answer:
d.tigers have a great IQR because they were some very heavy tigers.(high outliers)
A restaurant offers 6 choices of appetizer, 8 choices of main meal, and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
Step-by-step explanation:
For one course:
6+8+5=
Two courses with appetizers and main meals (* means times)
6*8
Two courses with appetizers and dessert
6*5
Two courses with main meals and dessert
8*5
The graph below shows the price of different numbers of beach balls at a store: Which equation can be used to determine p, the cost of b beach balls? b = 5.50p p = 5.50b p = 11b b = 11p
Answer:
p = 5.50b
Step-by-step explanation:
2 beach balls cost 11
4 beach balls cost 22
6 beach balls cost 33
So each (1) ball b costs 5.50 ($) p
Please Help...Anyone? I am revising for a test tomorrow, so please explain how you get the answer, too.. The ratios of the ages of Sunil and his Wife is 4:3. After 4 years, the ratio will be 9:7. What is the present age of Sunil
Answer:
32 years old
Step-by-step explanation:
Please see attached picture for full solution.
Let Sunil's present age be 4x and his wife's present age be 3x.
please help, tysm if you do
the length of a rectangle is 2 cm less than three times the width. the perimeter of the rectangle is 92 cm. find the dimensions of the rectangle. A. 11, 31 cm
B. 12, 34 cm
C. 12, 38 cm
D. 13, 37 cm
Answer:
I hope it will help you.......
Juan hiked to the top of a 3,000-foot mountain and back down without taking a break. Which graph best represents Juan's distance from the top of the mountain during the entire hike?
Answer:
Top left graph.
Step-by-step explanation:
If Juan didn't take a break, there is no plateau/flat line. And if he started hiking up and then down, then the graph should be an upside-down V shape.
Answer:
Graph A is the most acuurate
Find w please help me
Answer:
w = 77°
Step-by-step explanation:
From the picture attached,
WXYZ is a quadrilateral having 4 interior angles,
m∠y = 90°
Therefore, (2x - 10) = 90°
2x = 90 + 10
2x = 100
x = 50
Now, m∠z = (x + 15)° = 65°
m∠x = (3x - 22)° = 150 - 22
= 128°
Sum of interior angles of a polygon = (n - 2)×180°
where n = Number of sides of the polygon
If n = 4,
m∠u + m∠x + m∠y + m∠z = (4 - 2) × 180°
w + 128 + 90 + 65 = 360
w = 360 - 283
w = 77°
Therefore, measure of w = 77°
Line A has an x-intercept of -4 and a y-intercept of 8. What is its slope?
Answer:
Step-by-step explanation:
We can use the intercept form of the equation of a line, then solve for y.
Intercept form
x/(x-intercept) +y/(y-intercept) = 1
x/-4 +y/8 = 1
__
Solving for y, we have ...
-2x +y = 8 . . . . multiply by 8
y = 2x +8 . . . . add 2x
The coefficient of x is 2, so the slope is 2.
__
The graph shows you the rise is 8 for a run of 4, so ...
slope = rise/run = 8/4
slope = 2
Write a two-column proof. Given: <2 is congruent to <5; Segment AB is congruent to Segment DE Prove: Segment BC is congruent to Segment EC
Answer:
proof
Step-by-step explanation:
Statements
Reasons
<2 is congruent to <5; Segment AB is congruent to Segment DE
Given
<3≅<4
Vertical angle theorem
ΔCDB≅ΔCAE
AAS
Segment BC is congruent to Segment EC
CPCTC
The segment BC is congruent to segment EC and this can be proven by using the properties of a triangle and the given data.
Given :
Angle 2 is congruent to angle 5.Segment AB is congruent to Segment DE.The following steps can be used in order to prove that segment BC is congruent to segment EC:
Step 1 - Using the triangle properties it can be proven that segment BC is congruent to segment EC.
Step 2 - According to the vertical angle theorem, angle 3 is congruent to angle 4.
Step 3 - Now, according to the AAS (Angle Angle Side) postulate, triangle CDB is similar to triangle CAE.
Step 4 - So, according to the CPCTC, segment BC is congruent to segment EC.
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Pleasseeee help me It's for a test Mars is extremely far from the Earth. Scientists estimate that it could take astronoauts 245 days to travel from Earth to Mars. This is more than half of a year! Suppose astronauts travel to Mars when the distance between Earth and Mars is 108 million miles. If the trip takes 245 days, on average, how many miles would be traveled each day? In your calculator, write the large number as a multiple of a power of 10 to compute the answer. Round to the nearest mile.
Answer:
440,816 miles per day
Step-by-step explanation:
whats the cube root of 3375 by prime factorization
Answer:
15
Step-by-step explanation:
Prime factors of 3375 are 3, 3, 3, 5, 5, 5.
Since you need the ∛ of 3375, ∛3375=15
Answer:
15
Step-by-step explanation:
15x15x15=3375
The number of squares that are required to fill a rectangle of 512 cm by 108 cm, if each square of length 8 cm is _____________. a. 838 b. 864 c. 752 d. 440
Answer:
864
Step-by-step explanation:
512÷8=64
108÷8=13.5
64×13.5=864
Answer:
b) 864 squares
Step-by-step explanation:
A(rectangle) = 512cm x 108cm = 55296 cm²
A(square) = 8cm x 8cm = 64 cm²
Ar/As = 55296cm²/64cm² = 864 squares
can someone in here help me with this question I'm stuck and I don't know to do it
Answer:
Substitute -3,-2,-1,0,1,2,3 in d equation given to u at first to complete the table
What is the volume of the cone with a diameter of 4ft and height 4ft round to the nearest cubic foot
Answer:
67
Step - Step - Explanation
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the circle equations in general form with their corresponding equations in standard form. x2 + y2 − 4x + 12y − 20 = 0
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 6x − 8y − 10 = 0
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
(x + 2)2 + (y + 3)2 = 18
5x2 + 5y2 − 10x + 20y − 30 = 0
(x + 1)2 + (y − 6)2 = 46
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 + 2x − 12y − 9 = 0
Answer:
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
Step-by-step explanation:
This can be done using the completing the square method.
The standard equation of a circle is given by [tex](x - a)^2 + (y-b)^2 = r^2[/tex]
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex]
[tex]x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\[/tex]
Therefore, for [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex]
[tex]x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\[/tex]
Therefore, for [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex]
Divide through by 3
[tex]x^2 + y^2 + 4x + 6y = 5[/tex]
[tex]x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
Therefore, for [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex]
Divide through by 5
[tex]x^2 + y^2 - 2x + 4y = 6[/tex]
[tex]x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
Therefore, for [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex]
Divide through by 2
[tex]x^2 + y^2 - 12x - 8y = 4[/tex]
[tex]x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
Therefore, for [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For [tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex]
[tex]x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\[/tex]
Therefore, for[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
For Plato / Edmentum
Just to the test and got it right ✅
What is the 5th equivalent fraction to 1/11 ?
Answer: 5/55
Step-by-step explanation:
1/11 x 5 = 5/55
So, the fifth equivalent fraction to 1/11 is 5/55.
The 5th equivalent fraction should be [tex]5\div 55[/tex]
Calculation of the equivalent fraction:Since the fraction is [tex]1\div 11[/tex]
So here the 5th equivalent should be
[tex]= 1\div 11 \times 5\div 5[/tex]
= [tex]5\div 55[/tex]
Here 5 represent the numerator and 55 represent the denominator.
Therefore, we can concluded that The 5th equivalent fraction should be [tex]5\div 55[/tex]
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What is 220% of 400? A. 88 B. 880 C. 8,800 D. 88,000
Answer:
The correct answer is B. 880
Step-by-step explanation:
220%=2.2
2.2(400)=880
Answer:
B. 880
Step-by-step explanation:
220% × 400
= 220/100 × 400
= 88000/100
= 880
Please sb help and write it down on paper then send a pic❤️
Answer:
Step-by-step explanation:
1) We would determine the cube root of 27 and find its square.
Cube root of 27 = 3
3² = 9
Solution = 9
2) 36³ = 46656
√36³ = √46656 = 216
3) we would find the 5th roof of - 243 and find its cube
5th root of - 243 = - 3
- 3³ = - 27
Solution = - 27
4) Looking at the expression, 40⅔, we can see that
a = 2
b = 3
c = 40
Answer: 1) We would determine the cube root of 27 and find its square.Cube root of 27 = 33² = 9Solution = 92) 36³ = 46656√36³ = √46656 = 2163) we would find the 5th roof of - 243 and find its cube5th root of - 243 = - 3- 3³ = - 27Solution = - 274) Looking at the expression, 40⅔, we can see that a = 2b = 3c = 40
Step-by-step explanation:
Which property can be used to solve the equation? StartFraction d Over 10 EndFraction = 12 addition property of equality subtraction property of equality multiplication property of equality division property of equality
Answer:
multiplication property of equalityStep-by-step explanation:
Given the equation d/10 = 12. To get the value of d, the follwoing steps can be used to solve for the value of d;
Multiply both sides by 10
d/10 * 10 = 12*10
d = 120
It can be seen from the calculation above that multiplication operation was used to get the solution to the equation. It can therefore be concluded that the multiplication property of equality was used to solve the equation.
PLEASE HELP, AND PLAESE EXPLAIN!!!
Answer:
D. 22.5 sq. un.
Step-by-step explanation:
W divides BU so that there is a ratio of 1;2 meaning that there are 3 parts.
That means that 3 parts is BUV; we know that one of those parts is 4.5 sq. un. so 4.5*3=13.5 sq. un. - Also 4.5*2=9 to get WUV
V is the midpoint of the line BS so that means that BUV and UVS are equal
we know that BUV is 13.5 so we multiply that by 2 to get the whole triangle
=27
The last step is to get rid of BVW which we know is 4.5
27-4.5=22.5
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
11.67
Step-by-step explanation:
Data given in the question
∠ADC = 42°
∠BAC = 68°
Let us assume that AC be Y
Now
In ΔACD
tan 42° = AC ÷ CD = Y ÷ x ...............................(i)
In ΔACB
tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)
Now take the value of Y from the equation (ii)
Y = 26 ÷ Tan 68° ...................... (iii)
Now place the value of Y in equation (i)
So,
Tan 42° = 26 ÷ tan 68° × X
X = 26 ÷ tan 68° × Tan 42° ......................(iv)
Now placing the values of tan 42° and tan 68° in equation (iv)
So,
X = 26 ÷ 0.900 × 2.475
= 11.67
The tan 42° = 0.900
And, the tan 68° = 2.475
which of the following angles is coterminal with 5pi/3? pi/3, 2pi/3, 4pi/3, 5pi/3
Answer:
5pi/3
Step-by-step explanation:
For two angles to be co-terminal, one must differ from the other by a multiple of 2pi.
The angle of consideration is 5pi/3
Let us consider the options one by one and see if they differ from the angle of consideration by a multiple of 2pi.
5pi/3 - pi/3 = 4pi/3
5pi/3 - 2pi/3 = 3pi/3 = pi
5pi/3 - 4pi/3 = pi/3
5pi/3 - 5pi/3 = 0 = 0(2pi)
5pi/3 is co-terminal with itself
Find the solution of this system of equations
- 2x + 10y = -22
-2x - 4y = 6
Answer:
x = 1, y = -2
Step-by-step explanation:
- 2x + 10y = -22 _______(1)
-2x - 4y = 6 _______(2)
From (1),
10y + 22 = 2x
x = (10y + 22) / 2
x = 5y + 11 .______(3)
Substitute (3) into (2),
-2 ( 5y + 11) -4y = 6
-10y - 22 - 4y = 6
-14y = 6 + 22
-14y = 28
y = 28/ -14
y =-2
Substitute y = -2 into (3).
x = 5y + 11
x = 5(-2) + 11
x = -10 + 11
x = 1
Therefore, the solution is x = 1, y = -2.
What do the Nineteenth Amendment and the Indian Citizenship Act of 1924
have in common?
O A. They both affected American Indians directly.
O B. They both allowed certain Americans to own property.
O C. They both permitted free expression with some restrictions.
O D. They both provided suffrage to a group of Americans.
Answer:
D
Step-by-step explanation:
Suffrage is the right to vote, and the nineteenth amendment gave women the right to vote, and the indian citizenship act of 1924 gave native americans the right to vote