Rosa bought 8 cans of juice for herself and her friends.
To calculate how many cans of juice Rosa bought, we first need to calculate the total amount of money she gave the cashier:
2/3 of 15 quarters = (2/3) x 15 = 10 quarters (since each quarter is worth 25 cents,
10 quarters are worth 10 x 25 = 250 cents)
3/5 of 10 nickels = (3/5) x 10 = 6 nickels (since each nickel is worth 5 cents, 6 nickels are worth 6 x 5 = 30 cents)
Therefore, Rosa gave the cashier 250 + 30 = 280 cents.
Now, we need to find out how many cans of juice Rosa can buy with 280 cents:
1 can of juice costs 35 cents, so 280 cents can buy 280/35 = 8 cans of juice.
Therefore, Rosa bought 8 cans of juice for herself and her friends.
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Divide g by seven than multiply by six
Answer:
6/7x
Step-by-step explanation:
g/7 x 6 = 6/7 x
Answer: g / 7 x 6
Explanation:
How would you solve this integral? Supposedly, you take the U sub of x/3, and then resubtitute after solving for du and dx getting 3/sqrt(9-9u^2)du which you then take the integral of to get the standard arcsin(u). Is there a more general way of doing this, or do I have to remember this standard integral?
Answer:
Step-by-step explanation:
I NEED HELP! BRAINLEST!
Answer:
Area of the shape = 62.135 (units^2)
Step-by-step explanation:
To start, divide the shape into simpler parts.
A triangle (4 by 6)
A Rectangle (6 by 6)
A half Circle (Radius of 3) - take the height (6) and divide it by 2 (= 3)
First get the area of the Triangle. Base x Height / 2
4 x 6 = 24; 24 / 2 = 12;
Area of the Triangle is 12
Second get the area of the Rectangle. Length x Width
6 x 6 = 36
Area of the Rectangle is 36
Third get the area of the circle Pie x Radius ^2 (squared)
3.14 x (3 ^2) = 28.27
Now take the area of the whole circle and divide it by 2 to get the half circle
28.27 / 2 = 14.135; Area of the half Circle is 14.135
Add up all the areas to get the total for your shape.
12 + 36 + 14.135 = 62.135
I need help with this math problem
Answer:
This rectangle is shifted 1 unit to the left and then 4 units down. So the algebraic rule is (x - 1, y - 4).
Any help with this please?
Answer:
223
Step-by-step explanation:
i am in 6th grade
Robert is on a diet to lose weight before his Spring Break trip to the Bahamas. He is losing weight at a rate of 2 pounds per week. After 6 weeks, he weighs 205 pounds. Write and solve a linear equation to model this situation. There should be at least 3 lines of work.
Answer: Let x be the number of weeks since Robert started his diet, and let y be his weight in pounds. We know that he is losing weight at a rate of 2 pounds per week, so the slope of the line is -2 (negative because he is losing weight). We also know that after 6 weeks, his weight is 205 pounds, so we have the point (6, 205).
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - 205 = -2(x - 6)
Simplifying this equation gives:
y - 205 = -2x + 12
y = -2x + 217
Therefore, the equation that models Robert's weight loss is y = -2x + 217.
To find how much weight Robert will lose after 8 weeks, we substitute x = 8 into the equation:
y = -2(8) + 217
y = 201
Therefore, Robert will weigh 201 pounds after 8 weeks on his diet.
To check that this answer is reasonable, we can use the information that Robert is losing weight at a rate of 2 pounds per week. In 8 weeks, he would have lost:
2 pounds/week x 8 weeks = 16 pounds
205 pounds - 16 pounds = 189 pounds
Since 201 pounds is more than 189 pounds, our answer of 201 pounds after 8 weeks is reasonable.
So the completed work is:
Let x be the number of weeks since Robert started his diet, and let y be his weight in pounds.
We know that he is losing weight at a rate of 2 pounds per week, so the slope of the line is -2 (negative because he is losing weight).
We also know that after 6 weeks, his weight is 205 pounds, so we have the point (6, 205).
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - 205 = -2(x - 6)
Simplifying this equation gives:
y - 205 = -2x + 12
y = -2x + 217
Therefore, the equation that models Robert's weight loss is y = -2x + 217.
To find how much weight Robert will lose after 8 weeks, we substitute x = 8 into the equation:
y = -2(8) + 217
y = 201
Therefore, Robert will weigh 201 pounds after 8 weeks on his diet.
Step-by-step explanation:
find the center and radius of the circle given by this equation: x squared space minus space 10 x space plus space y squared space plus space 6 y space minus space 30 space equals space 0 what is the center?
The center and radius of a circle given by the equation x² - 10x + y² + 6y - 30 = 0 is (5,-3) and√64 = 8 units.
When finding the center and radius of a circle given by the equation x² - 10x + y² + 6y - 30 = 0, one can use the following steps:
The first step is to rearrange the equation into the standard form, (x - a)² + (y - b)² = r². This is done by completing the square for both the x and y terms in the equation.
x² - 10x + y² + 6y - 30 = 0x² - 10x + 25 + y² + 6y + 9 - 30 = 25 + 9(x - 5)² + (y + 3)² = 64 Therefore, the center of the circle is (5,-3), and the radius is √64 = 8 units.
Explanation: Given the equation x² - 10x + y² + 6y - 30 = 0, we want to find the center and radius of the circle. The standard form of the equation of a circle with center (a,b) and radius r is (x - a)² + (y - b)² = r². We will begin by completing the square for the x terms and the y terms separately: For the x terms: x² - 10x= x² - 10x + 25 - 25= (x - 5)² - 25 For the y terms: y² + 6y= y² + 6y + 9 - 9= (y + 3)² - 9 Now we can substitute these expressions back into the original equation and simplify: x² - 10x + y² + 6y - 30 = 0(x - 5)² - 25 + (y + 3)² - 9 - 30 = 0(x - 5)² + (y + 3)² = 64 The equation is now in standard form,
which means that the center of the circle is (5,-3) and the radius is √64 = 8 units.
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7. assume that the probability a child is a boy is 0.51 and that the sexes of children born into a family are independent. what is the probability that a family of five children has (a) exactly three boys?
The probability of having a boy is 0.51, and the probability of having a girl is 1 - 0.51 = 0.49. To find the probability of having three boys, we use the binomial probability formula: P(X = k) = (n choose k) * pk * (1-p)(n-k).
What is probability?Probability is an estimate of how likely an event is to occur. It is a value ranging from zero to one, with 0 indicating an impossible event and 1 indicating a certain event. The higher the likelihood, the more probable the event will occur, and the lower the probability, the less likely the event will occur.
The probability of having a boy is 0.51, which means that the probability of having a girl is 1 - 0.51 = 0.49.
We want to find the probability that a family of five children has exactly three boys. We can use the binomial probability formula:
P(X = k) = (n choose k) * [tex]p^k * (1-p)^(n-k)[/tex]
where:
P(X = k) is the probability of getting k successes (in this case, having k boys)
n is the number of trials (in this case, the number of children born)
p is the probability of success (in this case, the probability of having a boy)
(n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials
So, for this problem:
n = 5
k = 3
p = 0.51
P(X = 3) = (5 choose 3) * [tex]0.51^3 * 0.49^(5-3)[/tex]
= (10) * [tex]0.51^3 * 0.49^2[/tex]
= 0.234
Therefore, the probability that a family of five children has exactly three boys is 0.234, or about 23.4%.
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If JKLM is a rhombus, MK = 30, NL = 13, and m/MKL = 41°, find each measure.
The measures are: [tex]MK = 30[/tex]
[tex]NL = 13[/tex]
[tex]m/MKL = 41^\circ[/tex]
[tex]m/NLK = 41^\circ[/tex]
[tex]y \approx 17.79^\circ[/tex]
What opposite angles are congruent?In a rhombus, all sides are equal in length and opposite angles are congruent. Let's denote the measures as follows:
MK = 30 (Given)
NL = 13 (Given)
m/MKL = 41° (Given)
m/NLK = x (To be determined)
m/MKL = y (To be determined)
Since JKLM is a rhombus, we know that JM = KL and JK = ML. We can use the properties of a rhombus to find the values of x and y.
First, we can use the fact that opposite angles in a rhombus are congruent. Since [tex]m/MKL = 41^\circ[/tex] , then m/NLK (opposite angle) is also 41°.
Next, we can use the fact that diagonals of a rhombus bisect each other at a 90° angle. Since MK = 30 and NL = 13, the diagonals JL and KM intersect at their midpoint, which we can denote as O.
Using the properties of right triangles, we can form a right triangle JOM with JO = JK/2 = ML/2 (since JL is the diagonal and KM is its midpoint), OM = MK/2 = 30/2 = 15, and JM = JK = ML (since JK = ML in a rhombus).
Now we can use trigonometry to find the value of y. In right triangle JOM, we have:
[tex]sin(y) = OM/JM = 15/JM[/tex]
Since JM = KL (by the properties of a rhombus), and KL is a diagonal bisecting NL, we can use Pythagoras' theorem to find KL:
[tex]KL^2 = NL^2 + LK^2 = 13^2 + (MK/2)^2 = 13^2 + 15^2 = 169 + 225 = 394[/tex]
[tex]KL = \sqrt394[/tex]
So, we can substitute JM = KL = √394 in the equation for sin(y):
[tex]sin(y) = 15/\sqrt394[/tex]
Taking the inverse sine of both sides:
[tex]y = sin^(-1)(15/\sqrt394)[/tex]
Using a calculator, we can find the approximate value of y to be [tex]y ≈ 17.79^\circ.[/tex]
Therefore, the measures are: [tex]MK = 30[/tex]
[tex]NL = 13[/tex]
[tex]m/MKL = 41^\circ[/tex]
[tex]m/NLK = 41^\circ[/tex]
[tex]y \approx 17.79^\circ[/tex]
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Could someone please help me out? ‘Preciate it
The hypotenuse of the triangle is x = 10.
How to find the value of x?We can see that we have a right triangle, then we can use the trigonometric relation:
cos(a) = (adjacent cathetus)/hypotenuse
Replacing the known values:
cos(60°) =5/x
Solving for x we will get:
x = 5/cos(60°) = 10
That is the value of x.
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all tests of hypothesis are based on the assumption that select one: a. the null hypothesis is false and should be rejected b. the observed difference is important c. the null hypothesis is true d. type i errors are more serious than type ii errors
All tests of hypothesis are based on the assumption that the null hypothesis is true. C. the null hypothesis is true is the correct option.
In hypothesis testing, two hypotheses are compared:
The null hypothesis (H0) and the alternative hypothesis (Ha).The null hypothesis is the statement that is assumed to be true, while the alternative hypothesis is the statement that the researcher is trying to prove.
For example, if the researcher wants to test whether a new drug is effective in treating a certain disease, the null hypothesis would be that the drug has no effect, while the alternative hypothesis would be that the drug is effective.
In hypothesis testing, the researcher collects data and then analyzes it using a statistical test. The test produces a p-value, which is the probability of getting the observed data if the null hypothesis is true. If the p-value is less than a pre-determined level of significance (usually 0.05), the null hypothesis is rejected and the alternative hypothesis is accepted.If the p-value is greater than the level of significance, the null hypothesis is not rejected and the alternative hypothesis is not accepted.Therefore, all tests of hypothesis are based on the assumption that the null hypothesis is true option c is correct..
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Can someone plss help mee it would mean a lot
Answer:
Step-by-step explanation:
(1,-2) (-3,1)
1. y--1= -- 3/4 (x+3)
2. y= --3/4x--5/4
Find the volume of the prism.
A drawing of a square prism with length, width, and height labeled start fraction 7 over 10 end fraction inch.
The volume of the prism is 0.343 cubic inches.
What is Volume ?
Volume is a measure of the amount of space occupied by a three-dimensional object. It is the quantity of space that a solid object occupies in three dimensions. Volume is often expressed in cubic units, such as cubic meters, cubic centimeters, or cubic inches , depending on the system of measurement used.
To find the volume of a rectangular prism, we multiply its length, width, and height.
In this case, the length, width, and height of the prism are all 0.7 inch. Therefore, the volume of the prism is:
Volume = (length) x (width) x (height)
= (0.7 x (0.7) x (0.7)
= 0.343 cubic inches
Therefore, the volume of the prism is 0.343 cubic inches.
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the t distribution, compared to the z distribution, is select one: a. more skewed b. more peaked for small samples but increasingly like the z distribution as n increases c. bimodal d. flatter for small sample sizes but increasingly like the z distribution as n increases
The t-distribution becomes flatter as the sample size increases.
The t distribution, compared to the z distribution, is more peaked for small samples but increasingly like the z distribution as n increases.
The t-distribution :
A t-distribution is a symmetric distribution that is similar to the standard normal distribution, also known as the z-distribution.
It is a continuous probability distribution that is used to estimate population parameters when the sample size is small (less than 30) or when the population standard deviation is unknown.
The t-distribution has more variability than the standard normal distribution due to the smaller sample size.
For a given number of degrees of freedom, the t-distribution has more density in the tails than the standard normal distribution.
The z-distribution :
The standard normal distribution is also known as the z-distribution. It is a continuous probability distribution that has a mean of zero and a standard deviation of one.
The z-distribution is bell-shaped, with a median of zero, a mode of zero, and a mean of zero.
In conclusion, the t-distribution has a peakier curve than the z-distribution, especially for small sample sizes.
However, as the sample size increases, the t-distribution approaches the z-distribution.
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in each case, from the coordinates of the given point, write the rule of the quadratic function
a: (6, 216)
b: (-4, 128)
c: (7, -490)
d: (0.5, 8)
e: (-4.5, -40.5)
f: (8, 16)
g: 8, 1/2)
h: 9, 275.4)
I: (10, -48)
a: y = 6x²
b: y = 8x² + 64x + 128
c: y = -23x² + 322x - 1056
d: y = 64x² - 64x + 8
e: y = -9x² - 81
f: y = -4x² + 64
g: y = -2x² + 8x
h: y = 1.4x² - 25.2x + 118.4
i: y = -18x² + 180x - 680
Rewrite the expression in terms of sine and cosine and utilize the Fundamental Pythagorean Identity: sin²(x)+cos²(x)=1
Verify the identity using the Pythagorean Identity:
[tex]csc(x)+cot(x)=\frac{1}{csc(x)-cot(x)}[/tex]
Using the definition of cosecant and cotangent, the expression can be rewritten as 1/sine (x) + 1/cosine (x).
1/sine (x) + 1/cosine (x) = 1 confirms that the Pythagorean identity.
What is cosecant of an angle?The cosecant of an angle is defined as 1/sine (x), and the cotangent of an angle is defined as 1/cosine(x).
Using the definition of cosecant and cotangent, the expression can be rewritten as 1/sine (x) + 1/cosine (x).
Using the fundamental Pythagorean identity, which states that
sine²(x) + cosine² (x) = 1, the expression can be further simplified to
sine²(x) + cosine² (x) + 1/sine (x) + 1/cosine (x) = 1.
To verify the identity, we can substitute sine²(x) + cosine² (x) with 1, leaving us with 1 + 1/sine (x) + 1/cosine (x) = 1.
Simplifying further, we get 1/sine (x) + 1/cosine (x) = 1, which is the original expression. This confirms that the Pythagorean identity is true for the given expression.
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In Mrs. Franklin's kindergarten class, children make handprints in a round clay mold for their parents. The mold has a radius of 2 inches. What is the mold's circumference?
Answer:
4π (approx. 12.57) inches
Step-by-step explanation:
Equation to find circumference of a circle is πd, where d is the diameter of the circle.
d = 2r (radius)
d = 4
Circumference = πd
Circumference = 4π (inches)
Circumference ≈ 12.57 (inches)
need solution
attached below
The two solutions for the given equation in the interval are:
x = 0°
x = 159.1°
Which are the solutions of the given equation?Here we have the equation:
|1 + 3sin(2x)| = 1
Breaking the absoulte value part, we will get two equations, these are:
1 + 3sin(2x) = 1
1 + 3sin(2x) = -1
Now we need to solve these two, the first one gives:
3sin(2x) = 1 - 1
3sin(2x) = 0
Then we know that:
2x = 0°
x = 0°/2 = 0
the other equation gives:
1 + 3sin(2x) = -1
3sin(2x) = -1 - 1
3sin(2x) =-2
sin(2x) = -2/3
2x = Asin(-2/3)
2x = 318°
x = 318.2°/2 = 159.1°
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Which line of music shows a reflection?
Answer:
It would be the last one.
Step-by-step explanation:
hope this is correct
(a) solve the differential equation y' = (2/3)x √(1 − 9y2) (b) solve the initial-value problem y' = (2/3)x √(1 − 9y2) ; y(0) = 0
Therefore, y = (1/3) sin ((1/2)x²) is the solution of the initial value problem y′=(2/3)x√(1−9y²); y(0) = 0.
Solve the initial-value problem?To solve the differential equation y′=(2/3)x√(1−9y²)
The differential equation to be solved is: y′=(2/3)x√(1−9y²).
Here, we need to find y.
For this, we will separate the variables and integrate both sides. Integration gives us:
`∫1/(√(1−9y²))dy=∫(2/3)x dx`
.On integrating the left side, we will use u-substitution.
u = 3y → du = 3 dy
dy = (1/3) du → y = (1/3) u.
Now the equation becomes `∫du/(√(1−u²))=(2/3)∫xdx`.
Now, substituting u = sin t in the left integral, we have: `
∫du/(√(1−u²))
=∫cos(t)dt
=[sin⁻¹(u)]+C`.
So, the left-hand side is `
[sin⁻¹(u)]+C
= [sin⁻¹(3y)] + C`
Now, the right-hand side will be:
∫xdx=(1/2)x²+D`
On combining both sides, we get the solution to the differential equation as: `
[sin⁻¹(3y)]+C=(1/2)x²+D`
On solving for y, we get:
y = (1/3) sin ((1/2)x² + D' ) or y = (1/3) sin ((1/2)x²)
since we can choose D' = C.
To solve the initial value problem
y′=(2/3)x√(1−9y2); y(0) = 0
To solve the initial value problem
y′=(2/3)x√(1−9y2)
y(0) = 0
we will substitute x = 0, y = 0 in the general solution that we obtained in part .
y = (1/3) sin ((1/2)x²)
y = (1/3) sin ((1/2)0²) = 0.
So the required solution is y = (1/3) sin ((1/2)x²).
Therefore, y = (1/3) sin ((1/2)x²) is the solution of the initial value problem y′=(2/3)x√(1−9y²); y(0) = 0.
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An architect is designing a new windmill with four sails. In his sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails, point R, has coordinates (3,−6). He wants to make another sketch that shows the windmill after the sails have rotated 90° about their center of rotation. What would be the coordinates of R′?
The coordinates of R' when rotated 90° about their center of rotation is (-6, -3).
What is the geometry?Geometry is a branch of mathematics that deals with the study of shapes, sizes, relative positions of objects, and the properties of space.
The point R(3, -6) is located in the fourth quadrant as both the x-coordinate and y-coordinate are positive.
When the sails rotate 90 degrees clockwise, the point R will move to a new location R' in the third quadrant where both the x-coordinate and y-coordinate are negative.
To find the coordinates of R', we need to swap the x-coordinate and y-coordinate of point R and then negate the new x-coordinate.
That is, if R' has coordinates (x, y), then x = -6 and y = -3.
Hence, the coordinates of R' are (-6, -3).
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Find the value of x. *
43°
99°
2x°
A.28
B22.5
C.19
D.71
Answer:
A
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
99° is an exterior angle of the triangle , then
2x + 43 = 99 ( subtract 43 from both sides )
2x = 56 ( divide both sides by 2 )
x = 28
Solve the system by substitution. y= 9x
y= 8x+4
the solution of a system of linear equations is (4,36) with the help of the substitution method.
The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
The given system of equations is
[tex]y=9x\\y=8x+4[/tex]
We shall solve it with the help of the substitution method
Substitute the value of y in Equation 2
[tex]9x=8x+4\\9x-8x=4\\x=4[/tex]
Put the value of x in Equation 1
[tex]y=9*4=36[/tex]
Hence the solution of a system of linear equations is (4,36) with the help of the substitution method.
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Mrs. Chen bought a big tub of 250 plastic geometric pieces to use in her math classes. The pieces are all a similar size but different shapes. She randomly selects a handful of pieces from the tub. The table below shows the geometric shapes she selects.
Geometric shape Number selected
triangle 3
square 2
hexagon 2
pentagon 4
rectangle 2
Based on the data, estimate how many pentagons are in the tub.
If necessary, round your answer to the nearest whole number.
Answer:
To estimate the number of pentagons in the tub, we can use the proportion of pentagons in the sample of geometric shapes that Mrs. Chen selected and apply it to the total number of geometric shapes in the tub.
The proportion of pentagons in the sample is:
4 / (3 + 2 + 2 + 4 + 2) = 4 / 13 ≈ 0.31
We can assume that this proportion is representative of the entire tub of geometric shapes, and we can apply it to the total number of geometric shapes in the tub:
0.31 x 250 ≈ 77.5
Rounding to the nearest whole number, we can estimate that there are approximately 78 pentagons in the tub.
Therefore, the estimated number of pentagons in the tub is 78.
Find the surface area of a rectangular prism with dimensions of 6m by 4 m by 15
Thus, the surface area with the dimensions of a rectangular prism as 6m by 4 m by 15 m is found as: S = 348 sq. m.
Define about the rectangular prism:A rectangular prism is a 3 solid that is surrounded by 6 rectangular faces, 2 of which are the bases (the top face and bottom face), and the remaining 4 are lateral faces. It likewise has 12 edges and 8 vertices.
A rectangular prism is sometimes known as a cuboid because of its shape. A shoe box, an ice cream bar, or a matchbox are some instances of rectangular prisms in everyday objects.
Dimensions of rectangular prism :
Length l = 6mwidth w = 4 mheight h = 15 msurface area of a rectangular prism:
S = 2(lw + wh + hl)
S = 2(6*4 + 4*15 + 15*6)
S = 348 sq. m.
Thus, the surface area with the dimensions of a rectangular prism as 6m by 4 m by 15 m is found as: S = 348 sq. m.
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Answer: 50
Step-by-step explanation:
2*6+2*4+2*15=12+8+30=50
Pls help , my geometry teacher can't teach
Answer:
58 m
Step-by-step explanation:
The correct answer is 58.
To get the perimeter you add all the sides of the image, however, you are missing 2 values from the image.
If you make the shape into a square where all opposite sides are the same length, then you will see that one missing length is 6 m =(10m-4m).
The other missing number is 12 m which is base of 19 m - 7m that you are given on the top.
So you add the measurements (going clockwise starting at the top, 7+6+12+4+19+10=58 m
Answer:
58 m
Step-by-step explanation:
You want the perimeter of the L-shaped figure shown.
PerimeterThe perimeter is the sum of the side lengths. Here, a couple of lengths are missing from the diagram, but that doesn't prevent us finding the perimeter.
HorizontalThe horizontal lengths at the top have the same total length as the length at the bottom marked 19 m. This means the sum of all of the horizontal lengths is ...
2 × 19 m = 38 m
VerticalThe vertical lengths at the right side have the same total length as the vertical length at the left side, marked 10 m. This means the sum of all of the vertical lengths is ...
2 × 10 m = 20 m
TotalThe perimeter is the sum of the horizontal and vertical lengths:
P = 38 m + 20 m = 58 m
The perimeter of the figure is 58 m.
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PLEAE USE SUBSTITUTION METHOD and pleae explain it..
y= x+4
3x+y=16
Answer:
x=3, y=7
Step-by-step explanation:
Substituting the first equation y=x+4 into the second:
3x+(x+4)=16
Simplifying:
3x+x+4=16
4x+4=16
Subtracting 4 from both sides:
4x=12
Dividing both sides by 4:
x=3
We can now substitute x=3 into our first equation, y=x+4.
Substituting:
y=3+4
y=7
So, x=3, y=7
For each of the following, identify the conic section represented, then rewrite the conic section in vertex form. Submit your answers and all your work to your teacher.
[tex]x^{2} +y^{2} -2x-2y=1[/tex]
Given equation represents a circle with center at (1, 1) and vertex form [tex](x - 1)^2 + (y - 1)^2 = 2.[/tex]
What is circle?A circle is a closed shape in geometry that consists of all points that are equidistant from a central point called the center. A circle is defined by its radius, which is the distance from the center to any point on the circumference (outer boundary) of the circle. The diameter of a circle is twice the radius, and the circumference is the total distance around the circle.
According to the given information:The given equation [tex]x^2 + y^2 - 2x - 2y = 1[/tex]represents a conic section known as a circle.
To rewrite the given equation in vertex form for a circle, we need to complete the square for both x and y terms separately. The vertex form of a circle is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is the radius.
Let's complete the square for x and y terms:
[tex]x^2 - 2x + y^2 - 2y = 1[/tex]
Adding and subtracting the necessary terms to complete the square:
[tex]x^2 - 2x + 1 + y^2 - 2y + 1 = 1 + 1[/tex]
Rewriting the equation in vertex form:
[tex](x - 1)^2 + (y - 1)^2 = 2[/tex]
So, the conic section represented by the given equation is a circle with its center at (1, 1) and a radius of √2, and the vertex form of the circle is [tex](x - 1)^2 + (y - 1)^2 = 2.[/tex]
Therefore, Given equation represents a circle with center at (1, 1) and vertex form [tex](x - 1)^2 + (y - 1)^2 = 2.[/tex]
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how do I solve this?
The value of FG( SAY X) = x=131.
What are angles?An angle is the result of the intersection of two lines.
An "angle" is the length of the "opening" between these two beams.
Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.
In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.
The two primary components of an angle are the limbs and the vertex.
The joint vertex is the common terminal of the two beams.
According to our question-
35 - 3x + 2x + 14= 180
49-x=180
-x=180-49
x=131
The value of FG( SAY X) = x=131.
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how dies gross income differ from net income?
Answer: Gross income is the total amount of money earned before any deductions or taxes are taken out. Net income, on the other hand, is the amount of money left after all deductions and taxes have been taken out. In other words, net income is what you actually take home after all expenses have been accounted for.