∠6 = 43°
If two angles sum to 90 degrees, they are said to be complementary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). Angles 1 and 2 are complementary if their total of angles equals 90 degrees (i.e., ∠1 + ∠2 = 90°), and as a result, they are referred to as each other's complements.
Now as per the question the given angle is
∠8 = 47°
It is also given that ∠6 and ∠8 form are complementary angles. Therefore it means that the sum of both the angles will be 90°
∠6 + 47° = 90°
Now subtracting 47 from both sides we will get :
∠6 = 90 - 47 = 43°
Therefore, ∠6 = 43°
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Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C = 375.3 cm
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 59.73 cm and 119.46 cm, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle as 375.3 cm. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
375.3 cm = 2 × π × (Radius of the circle)
(Radius of the circle) = 375.3cm/ (2 × π)
The radius of the circle = 59.73 cm
Diameter of circle = 2 × (Radius of the circle)
= 2 × 59.73 cm
= 119.46 cm
Hence, the radius and the diameter of the circle are 59.73 cm and 119.46 cm, respectively.
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Use the order of operations to simplify each expression.
5[(2+5) / ]
Simplification of the given expression 5[(2+5) /35 ] using the order of operation PEDMAS is equal to 1.
As given in the question,
Given expression is 5[(2+5) /35 ]
Simplify the given expression using the order of operation PEDMAS,
5[(2+5) /35 ]
= 5[ 7/35]
= 5 [ 1/5]
=1
Therefore, simplification of the given expression 5[(2+5) /35 ] using the order of operation PEDMAS is equal to 1.
The complete question is :
Use the order of operations to simplify each expression.
5[(2+5) /35 ]
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Write an equation of each line.slope =5 ; through (0,2)
The equation of the line, with slope equal to 5 and passing through the point located at (0 , 2), is 5x - y = -2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 5 and (x1 , y1) = (0 , 2)
(y - 2) = 5(x - 0)
y - 2 = 5x
In slope-intercept form, the equation of the line is:
y - 2 = 5x
y = 5x + 2
In standard form, the equation of the line is:
y = 5x + 2
5x - y = -2
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Solve the word problems
1) There are 45 red balloons, 85 blue balloons and
120 yellow balloons. How many red and blue
balloons are there altogether?
(Show your work)
Answer:
add the red and the blue balloons
45+85=130
Given ABCD, solve for x.
Answer:
D. 1
Step-by-step explanation:
16+2x = 10+8x
6 = 6x
x = 1
BC and AD parallel and congruent (=) to each other
Write an explicit and a recursive formula for each sequence. 27,15,3,-9,-21, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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David has 10 cent pieces in one pocket and 25 cent pieces in the other pocket. if he has the same amount of money in each , what is the least amount he can have in each pocket
Solve each equation. t-2(3-2 t)=2 t+9
The solution of the given linear equation in one variable t - 2(3 - 2t) = 2t + 9 is at t = 5.
According to the given question.
We have a linear equation in one variable.
t -2(3-2t) = 2t + 9
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable t -2(3-2t) = 2t + 9 is given by
t - 2(3 - 2t) = 2t + 9
⇒ t - 6 + 4t = 2t + 9 (by distributive rule)
⇒ 5t - 6 = 2t + 9
⇒ 5t - 2t = 9 + 6
⇒ 3t = 15
⇒ t = 15/3
⇒ t = 5
Hece, the solution of the given linear equation in one variable t - 2(3 - 2t) = 2t + 9 is at t = 5.
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Write the specified type of proof.
flow proof
Given: K || LM, JL || KM
Prove: ΔJ M L≅ ΔM J K
We can state that ΔJML ≅ ΔMJK under SSS condition.
What specifically do we mean by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).
So,
Given: KJ || LM, JL || KM
To Prove: ΔJML ≅ ΔMJK
KJ = ML = (Given: equal)JL = KM = (Given: equal)JM = JM = (Common)So, ΔJML ≅ ΔMJK under SSS condition.
Therefore, ΔJML ≅ ΔMJK.
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Solve the following inequality algebraically.
x^2-3x-70< 0
Answer:
-7<x<10
Step-by-step explanation:
trust :)
At a local department store, sweaters are typically priced at $25. Due to a special, the sweaters are reduced to 80% of their original price. How much are the sweaters now? Round your answer to the nearest whole number if necessary.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The sweaters are now $20.
Step-by-step explanation:
$25 × .8 = $20
1 ton makes 90 cars
there are 280 million cars needed
1 ton = 500,000 gallons of water
figure out how much water is needed for 280 million cars.
What I have so far
500,000*280 million= 1.4*[tex]10^{14}[/tex]
Do i divide by 90 and am i even doing this correct?
The number of gallons required for 280 million cars is 1,555,556 gallons.
Given that, 1 ton makes 90 cars, there are 280 million cars needed
and 1 ton = 500,000 gallons of water.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of gallons of water needed for 280 million cars be x.
Now, 90 : 500,000 :: 280 : x
⇒ 90x=500,000 × 280
⇒ x = 14,00,00,000/90
⇒ x = 1,555,555.555≈1,555,556 gallons
Therefore, the number of gallons required for 280 million cars is 1,555,556 gallons.
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The points (8, 3) and (j, 5) fall on a line with a slope of -1/4. What is the value of j? help me ASAP
==================================================
Work Shown:
m = slope
m = (y2 - y1)/(x2 - x1)
m = (5 - 3)/(j - 8)
m = 2/(j - 8)
Plug in the given slope of -1/4 and solve for j
m = 2/(j - 8)
-1/4 = 2/(j - 8)
-1*(j-8) = 4*2
-j + 8 = 8
-j = 8-8
-j = 0
j = 0
The slope through (8,3) and (0,5) is -1/4
--------------
Check:
m = (y2 - y1)/(x2 - x1)
m = (5-3)/(0-8)
m = 2/(-8)
m = -1/4
The answer is confirmed.
Answer:
j = 0
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\large\boxed{y=mx+b}[/tex]
where:
m is the slope.b is the y-intercept.Given:
Slope = -¹/₄Point = (8, 3)Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx+b\\\implies 3 & = -\dfrac{1}{4}(8)+b\\3 & = -2+b\\3+2&=-2+b+2\\5&=b\\\implies b & =5\end{aligned}[/tex]
Substitute the given slope and found value of b into the formula to create an equation for the line:
[tex]\boxed{y=-\dfrac{1}{4}x+5}[/tex]
Substitute the point (j, 5) into the equation and solve for j:
[tex]\begin{aligned}y&=-\dfrac{1}{4}x+5\\\implies 5&=-\dfrac{1}{4}j+5\\5-5&=-\dfrac{1}{4}j+5-5\\0&=-\dfrac{1}{4}j\\\implies j&=0\end{aligned}[/tex]
Solution
Therefore, the value of j is 0.
What is the probability of rolling a number less than 3? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of rolling a number less than or equal to 3 is 0.5.
What is the probability of rolling a number?The likelihood of getting any side of the dice is 1/6 because there are six possible results. Rolling a 1 has a 1/6 chance of happening, a 2 has a 1/6 chance, and so on.The sum of the three probabilities equals 1/36, or the likelihood that all three will occur.A dice has only 6 sides, and only 1 of those sides is 6, meaning there are 16 chances to roll a 6.63 + 216 = total number of outcomes. When a die is rolled, there is a 1/6 chance of rolling a 4.What is the probability of rolling a number less than 3?
Event: The collection or the set of outcomes in an experiment is called as an event.
Outcomes: The possible results of a trail in an experiment are called as outcome.
Probability:
The ratio of the number of favorable outcomes to certain event and the total number of possible outcomes is called as the probability of an event.
The probability of rolling a number less than or equal to 3 is obtained by taking the ratio of the number of favorable outcomes by the total number of outcomes. It is expected about 50% of times that rolling a number less than or equal to 3.
The probability of rolling a number less than or equal to 3 is 0.5.
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with what force will a car hit a tree if the car has a mass of 3,000 kg and an acceleration of 2 m/s2
Answer:
6000 Newtons
Step-by-step explanation:
just multiply 3000 by 2
Points D and E are aligned with a ruler. Point D is at the mark of 4.5 cm, and the distance between points D and E is 3.4 cm. At which, two marks on the ruler could point E be located?
Answer:
E could be located at 7.9cm.
In the diagram, m∠BDA = 119° . Find m∠BDC
Answer: angle BCD is 77°
Step-by-step explanation:
BDC+CDA=119°
-5x+52°-2x+32°=119°
-7x+84°=119°
-7x=35°
x=-5°
Then substitute x in the equation for BDC
-5(-5)+52°=BDC
25+52°=BDC
BDC=77°
a. If T U=14 feet, what is the radius of ®Q ?
If TU = 14 feet, then the radius of the circle is 7 feet.
What is meant by radius?
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'.
A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length.
Simply dividing the circle's diameter in half yields the radius formula. If we connect the points on the circle's circumference to the exact center.
Let the radius of the circle be TU = 14 feet
Radius of the circle = c/2
Where, c = 14 then substitute the value in the above equation, then
r = 14/2
r = 7 feet
Therefore, the radius of the circle is 7 feet.
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2^4x2^-7
Solution_______________
Answer:
1/8
Step-by-step explanation:
What is y = -3x - 19 in Ax+By=C form?
The equation y = -3x - 19 (slope-intercept form) in Ax + By = C form is 3x + y = 19.
What is slope intercept form?The slope-intercept form of a linear equation is a way to express a linear equation in the form y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept.
According to the given information:
The given equation, y = -3x - 19, is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. However, to write it in the Ax + By = C form, also known as the standard form of a linear equation, we need to rearrange it.
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and A is usually required to be a positive integer or zero.
To convert y = -3x - 19 into standard form, we can follow these steps:
Step 1: Move all the terms to one side of the equation.
y + 3x = -19
Step 2: Multiply all the terms by -1 to make the coefficient of x positive.
-1(y + 3x) = -1(-19)
-y - 3x = 19
Step 3: Rewrite the equation with positive coefficients for x and y.
3x + y = 19
So, the equation y = -3x - 19 in Ax + By = C form is 3x + y = 19.
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Please Help if pQ = 6n QR=3 and PR=27 find n and PQ
Answer:
4
Step-by-step explanation:
PR - QR = PQ
27 - 3 = 24 =PQ
24=6n
n=4
Find following measure.
m WX
When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.
The measure of m WX is 66.
What is meant by inscribed arc?The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.
Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.
According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.
In the given diagram, XY is a semi-circle. So,
m XWY = 180
m WX + m WY = 180
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
m WY = 2(m ∠X)
m WY = 2(m ∠X) = 114
Therefore, m WX = 180 - m WY = 66.
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Find m/_1 and m/_2. Justify each answer
The average sale price (online) for a certain brand of professional mountain bike is approximately normally distributed with a mean of $4,200 and a standard deviation of $250.
Find the 30th percentile of this distribution.
According to the question, for the average sale price the given parameters are mean as $4200 and standard deviation as $250.
As per normal distribution, the standard formula is as written below:
[tex]z = \frac{value - mean}{SD}[/tex]
And through normal distribution, the value of z = -0.52 which gives the area of the left bounded.
Now, substitute the values in the given expression, we get:
[tex]-0.52=\frac{x-4200}{250}[/tex]
Now the calculated value of 'x' = $4070.
To calculate the 30 percent of the mountain bike, the sale price will be $4068.90.
Therefore, the 30th percentile of the distribution is $4068.90.
What is normal distribution?
The normal distribution play a vital role in statistics. It measured the data which occurred very frequently and it is close to the mean value of the data. And it is of bell shaped.
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Compare and contrast the perpendicular bisectors, medians, and altitudes of a triangle.
The perpendicular bisector of a segment is a line that passes through the midpoint of a segment and is perpendicular to the segment.
What is the difference between perpendicular bisectors, medians, and altitudes of a triangle?
A perpendicular bisector is a line that intersects and passes through the midpoint of a given segment at a 90° angle.
A triangle's median is a line segment that connects a vertex to the opposing side's midpoint. Every triangle has three medians, one from each vertex, and they all cross at the triangle's centroid.
A triangle's altitude is a line segment that passes through a vertex and is perpendicular to the baseline.
Median: A median is a segment that connects a vertex to the midpoint of the opposite side.Altitude: Altitude is defined as the perpendicular distance from a vertex to the opposite side.Perpendicular Bisector: The perpendicular bisector of a segment is a line that passes through the midpoint of a segment and is perpendicular to the segment.To learn more about perpendicular bisector refer to:
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Find the scale factor used to dilate quadrilateral LOVE, L (0,-7), O (5,-4), V (1,-5), E (3, -1) to L'O'V'E', L' (0, -21), O' (15, -12), V' (3, -15), E' (9,-3).
Answer:
7142213126 LOVE
Step-by-step explanation:
i dont no what i am doing this answer is wrong
Two similar cylinders have heights of 35 meters and 25 meters. What is the ratio of the volume of the large cylinder to the volume of the small cylinder?
The ratio of the volumes of two similar cylinders with heights of 35 meters and 25 meters, respectively, is 2.744.
Solids of the same type that have proportional corresponding linear
measures are similar solids. In the case of similar cylinders:
height of A/ height of B = radius of A/radius of B
If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
volume of A/ volume of B = (height of A/ height of B)^3 = (radius of A/radius of B)^3
If two similar cylinders have heights of 35 meters and 25 meters, then the ratio of the volume of the large cylinder to the volume of the small cylinder is:
height of larger cylinder / height of smaller cylinder = 35 meters / 25 meters = 7/5
volume of larger cylinder/ volume of smaller cylinder = (height of larger cylinder / height of smaller cylinder)^3 = (7/5)^3 = 2.744
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y=-|x|
where does that go on a graph ?
What is the product of 48.65(6.2)?
Answer:
48.65x6.2=301.63
Step-by-step explanation:
Answer:
down below
Step-by-step explanation:
301.63
It's a bit difficult to type this in a mobile so I won't put it. If you would like the explanation, I can always go back and edit my answer
Hope this helps! :)
which value of x makes lines r and s parellel
Answer:
75
Step-by-step explanation:
If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel
x + 25 + 80 = 180
x = 180 - 80 - 25
x = 75
