The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.
How do you solve for the larger acute angle of ΔABC ?Let's denote the angles of triangle ΔABC as follows:
∠A = x
∠B = y
∠C = 90° (right-angled triangle)
Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.
Since CD is the median, we know that angle ∠ECD = φ.
In right-angled triangle ΔCEB, we have:
∠CEB = 90° - y
Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:
∠CED + ∠CEB + ∠ECD = 180°
Substitute the known values:
∠CED + (90° - β) + φ = 180°
Since ∠CED and ∠A are supplementary angles, we can also write:
∠CED = 180° - x
Now substitute this value into the previous equation:
(180° - x) + (90° - y) + φ = 180°
Simplify the equation:
270° - x - y + φ = 180°
Subtract 90° from both sides:
180° - x - y + φ = 90°
From this equation, we get:
x + y = 90°
Substitute this value back into the equation involving φ:
180° - (90°) + φ = 90°
Simplify:
90° + φ = 90°
Therefore, the measure of the larger acute angle of ΔABC is:
x = 45° + φ/2 (option a)
the above answer is in response to the full question below;
Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:
a. 45⁰ + φ/2
b. 60⁰ + φ/2
c. 90⁰ - φ/2
d. 2φ
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please help! it is matrices, so it should be rlly easy.
B is a 2 by 2 matrix, and the determinant of B written as |B| is equal to -1.
How to find the determinant of the matrix BWe can find |B|, the determinant of the matrix B by subtracting the multiple of row column and row 2 column 1 from the multiple of row column 1 and row 2 column 2 as follows:
|B| = (-2 × -2) - (1 × 5)
|B| = 4 - 5
|B| = -1.
Therefore, the determinant of the 2 by 2 matrix B written as |B| is equal to -1.
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50 Points! Solve each equation or inequality. Only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!
The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41 and the solution to the inequality is b ≤ 1.87
Solving the equations or inequalities for wFrom the question, we have the following parameters that can be used in our computation:
5ʷ ⁺ ³ = 17
Take the logarithm of both sides
So, we have
w + 3 = ln(17)/ln(3)
Evaluate the quotient
This gives
w + 3 = 2.59
So, we have
-3 + w + 3 = 2.59 - 3
Evaluate
w = 0.41
For the second expression, we have
2ᵇ ⁺ ¹ ≤ 7.31
Take the logarithm of both sides
So, we have
b ≤ ln(7.31)/ln(2) - 1
So, we have
b ≤ 1.87
Hence, the equation when solved for w is approximately w = 0.41
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Find the sum:
125 (base 7) + 256 (base 7)
The sum of 125 (base 7) and 256 (base 7) is 404 (base 7). To compute it, we convert each number to base 10, add them, and then convert the result back to base 7.
Write each number in expanded form using powers of 7.
125 (base 7) = 1 x 7² + 2 x 7¹ + 5 x 7⁰ = 49 + 14 + 5 = 68
256 (base 7) = 2 x 7² + 5 x 7¹ + 6 x 7⁰ = 98 + 35 + 6 = 139
Add the two numbers together to get the sum in decimal form.
68 + 139 = 207
Convert the decimal sum to base 7 using repeated division by 7.
Divide 207 by 7 to get a quotient of 29 and a remainder of 4. Write down the remainder as the rightmost digit in the base 7 representation. Divide 29 by 7 to get a quotient of 4 and a remainder of 1. Write down the remainder as the next digit to the left in the base 7 representation.
Divide 4 by 7 to get a quotient of 0 and a remainder of 4. Write down the remainder as the leftmost digit in the base 7 representation.
So the sum of 125 (base 7) and 256 (base 7) is 404 (base 7).
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Find the endpoints of the latus rectum of the parabola below.
(y - 1)? = 16(x + 1)
Answer:
(3, 9) and (3, -7)
Step-by-step explanation:
You want the end points of the latus rectum for the parabola defined by ...
(y -1)² = 16(x +1)
Vertex and scale factorCompare the given equation to the form ...
(y -k)² = 4p(x -h)
we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.
Latus rectumSince the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...
(h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)
__
Additional comment
If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).
On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).
What is the standard form of the equation for the circle
A. (X-3)^2+(y-2)^2=32
The standard form of the equation for the circle is (x - 3)² + (y - 2)² = 8.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = √[(3 - 5)² + (2 - 4)²] = √8
Center, (h, k) = (3, 2).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 3)² + (y - 2)² = (√8)²
(x - 3)² + (y - 2)² = 8.
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Complete Question:
A circle is shown on the coordinate plane. The graph shows a circle with the origin point A at (3, 2), and a point B on its circumference at (5, 4) and intersects the x-axis at 1 and 5 units. What is the standard form of the equation for the circle?
Please help me!
Which of these graphs represent a function?
Answer:
X
Step-by-step explanation:
You want to identify the graph that represents a function.
Vertical line testA graph represents a function if no vertical line intersects the graph in more than one place.
W – the line x=0 intersects the graph at y = -4 and at y = 4. This graph is not the graph of a function.
X – At points where the graph might overlap, one point is identified as not include, (1, -1) for example, while the other point is identified as included (1, 1) for example. This means there is only one function value at that point, so this is the graph of a function.
Y – The vertical line x=-2 intersects the graph in an infinite number of points. This graph is not the graph of a function.
Z – The vertical line x=0 intersects the graph at y = -2, y = 0, and y = 2. This graph is not the graph of a function.
<95141404393>
CNNBC recently reported that the mean annual cost of auto insurance is 957 dollars. Assume the standard deviation is 193 dollars. You will use a simple random sample of 58 auto insurance policies. You may assume original population is approximatley normally distributed, and round your answers to three decimals.
Find the probability that a single randomly selected policy has a mean value between 964.6 and 1000.1 dollars.
P(964.6 < X < 1000.1) = ???
Find the probability that a random sample of size
has a mean value between 964.6 and 1000.1 dollars.
P(964.6 < M < 1000.1) = ???
The probabilities are given as follows:
P(964.6 < X < 1000.1) = 0.071 = 7.1%.P(964.6 < M < 1000.1) = 0.338 = 33.8%How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for this problem is given as follows:
[tex]\mu = 957, \sigma = 193[/tex]
The probability is the p-value of Z when X = 1000.1 subtracted by the p-value of Z when X = 964.6, hence:
Z = (1000.1 - 957)/193
Z = 0.22.
Z = 0.22 has a p-value of 0.5871.
Z = (964.6 - 957)/193
Z = 0.04.
Z = 0.04 has a p-value of 0.5160.
Hence:
0.5871 - 0.5160 = 0.0711.
For the sample of 58, the standard error is obtained as follows:
s = 193/sqrt(58) = 25.34.
Hence:
Z = (1000.1 - 957)/25.34
Z = 1.7.
Z = 1.7 has a p-value of 0.9554.
Z = (964.6 - 957)/25.34
Z = 0.3.
Z = 0.3 has a p-value of 0.6179.
Hence:
0.9554 - 0.6179 = 0.338.
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A group of students worked out the mean and range of their ages. The mean was 12 years and 3 months. The range was 2 years and 7 months. a) What was the mean of the ages of the same group of students exactly one year later? b) What was the range of their ages exactly one year later? Write a sentence to explain each of your answers.
Exactly one-year later,
(a) Mean of the ages will be 13 years and 3 months.
(b) Range of the ages will be same 2 years and 7 months.
Part (a) : To find the mean of the ages of the same group of students exactly one year later, we add one year to each student's age and find the new mean.
New mean is : 12 years and 3 months + 1 year = 13 years and 3 months;
So the mean of the ages of the same group of students exactly one year later is 13 years and 3 months.
Part (b) : The range of their ages would still be 2 years and 7 months because we are adding the same amount to all of their ages, the difference between the youngest and oldest member of the group would remain the same.
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i need answer please
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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Suppose we have a large population with mean and standard deviation . Let’s say we randomly sample 100 values from this population and compute the mean, then repeat this sampling process 10,000 times and record all the means we get. Which of the following is the best approximation for the standard deviation of our 10,000 sample means?
The best approx. for mean of 10,000 sample means is equal to the population mean which is 84. The Option C is correct.
What is best approx. for mean of 10,000 sample?According to central limit theorem, the distribution of sample means from a large sample size will be normal regardless of the shape of the population distribution.
This is because the mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
The standard deviation of distribution of sample means will be:
= Population standard deviation / √sample size
= 7.2 / √100
= 0.72
So, the best approximation for the mean of 10,000 sample means is equal to the population mean which is 84.
Full question "Suppose we have a large population with mean = 84 and standard deviation = 7.2. 10 points Let's say we randomly sample 100 values from this population and compute the mean, then repeat this sampling process 10,000 times and record all the means we get. Which of the following is the best approximation for the mean of our 10,000 sample means? A. 8.4 b. 100 c. 84"
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someone pls help me with this question!!
Answer:
x < -1 or x ≥ 5
Step-by-step explanation:
You want the solution and its graph for the compound inequality ...
3x -2 < -5, or-2x ≤ -10SolutionAdding 2 to the first inequality gives ...
3x < -3
x < -1 . . . . . divide by 3
Multiplying the second inequality by -1/2 gives ...
x ≥ 5
The solution is x < -1 or x ≥ 5.
someone help i really need help with this
Answer:
29
Step-by-step explanation:
she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.
need help please
here is the picture is about Row Ops
The result of adding -3 (row 1) to row 2 is determined as (0 10) |-14.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 -4] | 8
To multiply row1 by -3, we will multiply each entity by 3 as shown below;
= -3(1 -4) | 8
= (-3 12) | -24
To add the result to 3;
(-3 12) | -24 + (3 -2)|10
= (0 10) |-14
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.
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how to find the area of a circle with the diameter of 22 in with pi
The area of the circle with a diameter of 22 in in terms of pi is 121π in².
What is the area of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
Where r is radius and π is constant pi.
Given that:
The diameter of the circle is 22 inches.
Radius is half of diameter
Hence:
Radius r = diameter/2 = 22/2 = 11 in
Plug the value into the above formula and solve for area.
A = πr²
A = π × ( 11 in )²
A = 121π in²
Therefore, the area is 121π in².
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If Kayla has a 73% in her history class and she took a test 20% of her grade and got a 60 on it. What would her grade be?
Answer:
70.4%
Step-by-step explanation:
Assuming the test is the only graded assignment, and the remaining 80% of her grade is still at 73%, we can calculate Kayla's new overall grade as follows:
New overall grade = (0.80 x 73) + (0.20 x 60)
New overall grade = 58.4 + 12
New overall grade = 70.4
Therefore, Kayla's new overall grade is 70.4%
Answer:
70.4% or a C-.
Step-by-step explanation:
To calculate Kayla's new grade after taking the test, you need to first find out what percentage of her overall grade the test is worth. If the test is worth 20% of her grade, then the remaining 80% of her grade is based on other factors, such as homework, quizzes, and other tests.
To calculate Kayla's new grade, you can use the following formula:
New grade = (Current grade x Weight of current assignments) + (Grade on test x Weight of test)
Plugging in the numbers given in the problem, we get:
New grade = (0.73 x 0.80) + (0.60 x 0.20)
New grade = 0.584 + 0.12
New grade = 0.704
Therefore, Kayla's new grade after taking the test would be approximately 70.4%, or a C-.
Can someone help with this and give the right answer I am on a time limit
The constant of variation, k, is defined as the ratio between the two variables' values, multiplied by their respective powers: [tex]k = y/x^a \times z/x^b,[/tex] where a and b are the powers of x in the expressions for y and z, respectively. when [tex]x = -3[/tex] and [tex]y = 4[/tex] , z is equal to -81/16.
What is the constant of variation?In this case, we have x = 8, y = 54, and z = 144, so we need to determine the powers of x in the expressions for y and z:
[tex]y = 54 = (8^a) \times k = > a = 3[/tex]
[tex]z = 144 = (8^b) \times k = > b = 2[/tex]
Substituting these values into the formula for k, we get:
[tex]k = y/x^a \times z/x^b = 54/8^3 \times 144/8^2 = 27/64[/tex]
Therefore, the constant of variation is 27/64.
Using the same formula as above, we can solve for z when x = -3 and y = 4:
[tex]k = y/x^a \times z/x^b[/tex]
We need to determine the powers of x in the expressions for y and z:
[tex]y = 4 = (-3)^a * k = > a = -1[/tex]
[tex]z = ? = (-3)^b * k = >[/tex] we don't know b or z yet
Substituting these values into the formula for k, we get:
[tex]k = y/x^a * z/x^b = 4/(-3)^(-1) * z/(-3)^b = -12z/(-3)^2[/tex]
Simplifying this expression, we get:
[tex]k = -12z/9 = -4z/3[/tex]
Now we can solve for z:
[tex]-4z/3 = 27/64[/tex]
Multiplying both sides by 3/(-4), we get:
[tex]z = -81/16[/tex]
Therefore, when [tex]x = -3[/tex] and [tex]y = 4, z[/tex] is equal to [tex]-81/16.[/tex]
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1. The rectangle shown is dilated by a scale factor of 3. (a) Calculate the length of each side of the dilated image. (b) Draw the new image and label it .
According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.
How to calculate the length of each side of the dilated image?To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:
8 / 3 = 2.6615 / 3 = 5According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.
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Please help solve graphs
The graphs are:
1) not one-to-one
2) one-to-one
3) not one-to-one
Are the graphs one-to-one?A graph represents an one-to-one function only if.
We can't draw a vertical line that touches the graph twice or more.
We can't draw an horizontal line that touches the graph twice or more.
For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.
Similarly forthe third graph, the line y = 0 touches two points-
So these two are not one-to-one.,
For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.
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The hypotenuse of a certain right triangle is twice the length of the
shorter leg. The shorter leg is 4 cm.
Answer:
Step-by-step explanation:
If the hypotenuse of a right triangle is twice the length of the shorter leg and the shorter leg is 4 cm, then the hypotenuse is 2 * 4 cm = 8 cm.
Using the Pythagorean theorem, we can find the length of the longer leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Letting c represent the length of the hypotenuse and a and b represent the lengths of the other two sides, we can write this as c^2 = a^2 + b^2.
Substituting in the known values for c and one of the other sides (let’s say a), we have:
8^2 = 4^2 + b^2 64 = 16 + b^2 b^2 = 48 b = sqrt(48)
So, the length of the longer leg is sqrt(48) cm, or approximately 6.93 cm.
Solve the following by completing the square or squaring both sides using steps illustrated in the lesson content.. Leave answers in radical (EXACT) form. Do not use decimals. -2x+6=-x^2
Answer:
Starting with the equation:
-2x + 6 = -x^2
First, we can rearrange it to put it in standard quadratic form:
x^2 - 2x - 6 = 0
To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:
x^2 - 2x + 1 - 1 - 6 = 0
The first three terms can be written as a perfect square:
(x - 1)^2 - 7 = 0
Add 7 to both sides:
(x - 1)^2 = 7
Now we can take the square root of both sides:
x - 1 = ±√7
Add 1 to both sides:
x = 1 ± √7
So the solutions to the equation are:
x = 1 + √7 or x = 1 - √7
mark me brilliant
How much work does an elevator motor need to do to lift a 1400kg elevator a height of 100m?
ans. 1400000
we know that
work done by gravity = mgh
just putting values we get
= 1400x 100 x 10
= 1400000
hence,work done an elevator motor need to do to lift a 1400kg elevator a height of 100m is 1400000
The angle of depression from the window of a building to a parked car is 38°. If the car is parked 320 feet away from the base of the building, what is the distance between the window and the car to the nearest tenth?
Answer:
Set your calculator to degree mode.
Please sketch the figure to confirm my answer.
cos(38°) = 320/d
d•cos(38°) = 320
d = 320/cos(38°) = 406.1 feet
v=? image attached please help
Answer:
v=12
Step-by-step explanation:
9/v = 6/8
9 = 6v/8
72= 6v
v= 12
Answer:
v = 12
Step-by-step explanation:
Now we have to,
→ Find the required value of v.
Given proportion,
→ (9/v) = (6/8)
Then the value of v will be,
→ (9/v) = (6/8)
→ 9 × 8 = 6 × v
→ 72 = 6v
→ 6v = 72
→ v = 72/6
→ [ v = 12 ]
Hence, the value of v is 12.
Find the real or imaginary solutions of the following equation by factoring.
w³-512=0
Choose the correct answer below.
OA. -8,4+4√3i, 8-4√3i
OB. 64,- 64+8i, 64-8√3i
O C. -512, -4+4√3i, -8-4√3i
OD. 8, -4+4√3i, -4-4√3i
You start at (2, -1). You move left 4 units. Where do you end?
Answer:
(-2, -1)
Step-by-step explanation:
You want the point that is 4 units left of (2, -1).
X-coordinateThe x-coordinate of an (x, y) coordinate pair tells you the number of units to the right of the x=0 point. It increases for points farther right, and decreases for points farther left.
Moving left 4 units decreases the x-coordinate by 4 units. The x-coordinate of 2 becomes ...
2 -4 = -2
The coordinates of the moved point are (-2, -1).
<95141404393>
The masses, in kilograms, of 25 pumpkins were
recorded and summarized in the histogram shown. No
pumpkin's mass was an integer number of kilograms.
How many pumpkins had a mass greater than
6 kilograms?
Observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.
What is a histogram?A histogram is a graph that displays the values of a numeric variable's distribution as a collection of bars.
The height of a bar represents the frequency of data points with values falling within the relevant bin; each bar typically spans a range of numerical values known as a bin or class.
Similar to a bar chart, a histogram is produced with bars of varying widths.
In a histogram, the frequency is revealed by the bar's area rather than its height.
We plot the frequency density rather than frequency on the y-axis. To figure this out, divide a group's frequency by its width.
So, the x-axis of the given histogram represents the mass of the pumpkins.
The y-axis of the histogram represents the number of pumpkins.
Then, the pumpkins with greater mass than 6 kilograms:
= 8 + 6 + 2
= 16
Therefore, observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.
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help this assignment is already past due
The decimals as a power of 10 are given as follows:
Decimal: [tex]1 x 10^{-1}[/tex]Centimeter: [tex]1 x 10^{-2}[/tex]Millimeter: [tex]1 x 10^{-3}[/tex]Micrometer: [tex]1 x 10^{-6}[/tex]What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
Hence the numbers are represented as follows:
Decimal: [tex]1 x 10^{-1}[/tex] -> the one is the first decimal digit.Centimeter: [tex]1 x 10^{-2}[/tex] -> the one is the second decimal digit.Millimeter: [tex]1 x 10^{-3}[/tex] -> the one is the third decimal digit.Micrometer: [tex]1 x 10^{-6}[/tex] -> the one is the sixth decimal digit.More can be learned about scientific notation at https://brainly.com/question/5756316
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I NEED HELP ASAP I have to tern this packet in tomorrow and i do not know how to solve scales in geometry
Answer:
The anser is letter C)
Step-by-step explanation:
because it multiplies x3
0,5×3=1,5
1,5×10=15
10×3=30
Answer:
1cm=30m
PLEASE HELP ITS DUE TOMORROW!!!
Answer:
Step-by-step explanation:
House
B) Down Payment: $151,800
C) $607,200
D) $819,720
E) $1,426,920
F) $47,564
Car:
B) $2,902.50
C) $16,447.50
D) $3,700.6875 = $3,700.69
E) $20,148.1875 = $20,148.19
F) $335.803125 = $335.80
DONE !!! :)
Help me please, this assignment is alr past due
Answer:
Step-by-step explanation:
However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent. Negative version because to get to a decimal you move in the negative direction.
.1 = 1.0 x [tex]10^{-1}[/tex]
.01 = 1.0 x [tex]10^{-2}[/tex]
.001 = 1.0 x [tex]10^{-3}[/tex]
.000001 =,1.0 x [tex]10^{-6}[/tex]