Answer:
C. [2, + ∞)-----------------
Given function:
g(x) = | x + 3| + 2We know that absolute value is non-negative, hence |x + 3| has a minimum value of 0 when x = - 3. Then the function has a minimum value of 2.
The range is the set of output values. As we see given function has a minimum value of 2 and no maximum value.
It can be shown as:
g ∈ [2, + ∞)The matching choice is C.
Need help asap
A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 4 tables is $37. The total cost to rent 3 chairs and 2 tables is $17.
What is the cost to rent each chair and each table?
Cost to rent each chair: SI
Cost to rent each table:
Solving a system of equations we can see that the costs are:
For a chair, 3/2 dollars.
For a table, 25/4 dollars.
What is the cost to rent each chair and each table?Here we can define the variables:
x = cost of rending a chair.
y = cost of renting a table.
Here we can write a system of equations:
8x + 4y = 37
3x + 2y = 17
We can subtract two times the second equation from the first one:
8x + 4y - 2*(3x + 2y) = 37 - 2*17
2x = 3
x = 3/2
And the value of y is:
3*(3/2) + 2*y = 17
2y = 17 - 9/2 = 25/2
y = 25/2/2
y = 25/4
These are the costs in dolllars.
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total population = 8,000,000
civilian labor force = 4,000,000
number of unemployed individuals who are actively seeking jobs = 400,000
number of unemployed individuals who are not seeking work 100,000.
This information indicates that country y's unemployment rate equals.
The given information indicates that country y's unemployment rate equals 10 %.
How to find the unemployment ?The formula to calculate the unemployment rate is:
Unemployment Rate = ( Number of Unemployed Individuals / Civilian Labor Force ) × 100
In this case, the number of unemployed individuals actively seeking jobs is 400,000, and the civilian labor force is 4,000,000.
Unemployment Rate = ( 400, 000 / 4, 000, 000) × 100
Simplifying the calculation :
= 0. 1 x 100
= 10 %
In conclusion, the unemployment rate in Country Y is 10%.
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1-56.
The owner of Universal Widgets has two teams of employees and
wants to know which team is working the "best." The assistant
manager gathered data for the number of widgets made per team
member on various days. He presented the data to the owner as
two boxplots, shown at right. The owner is confused.
a. Help the owner decide which team is working the "best"
by comparing center, shape, spread, and outliers.
b. Which team had a smaller standard deviation? Explain.
200
150
100
30
Team I
Name an equation parallel to: y = -2/3 x + 10
Answer: The answer is...
y = -2/3 x + 1
Step-by-step explanation:
The others would have crossed paths with y = -2/3 x + 10
HELP PLEASEE PLEASE I NEED TO PASS THIS LESSON
The function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.
The given table is
Days After Number of
Release Date Games sold
0 1024
1 512
2 256
3 128
Here, the common ratio = 512/1024
= 1/2
The formula to find nth term of the geometric sequence is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.
Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]
Therefore, the function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.
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The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45cm 7mm when they are born, What is the height of the average fourth grader?
The height of the average fourth grader is 137cm 1mm. This height can be determined by multiplying 3 by the average height of a newborn baby.
Given information,
The average height of babies = 45 cm 7mm
45 cm 7 mm is equivalent to 45.7 cm (since there are 10 millimeters in a centimeter).
Let the height of a fourth grader be x.
According to the question,
The height of a fourth grader (x) = 3 × the average height of a newborn baby
The height of a fourth grader (x) = 3 × 45.7
The height of a fourth grader (x)= 137.1 = 137cm 1mm
Therefore, the height of a fourth grader is 137cm 1mm.
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From the observation deck of a skyscraper, Morgan measures a 67^{\circ}
∘
angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
The Horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.
We can use trigonometry and the concept of angles of depression. We can consider the height of the observation deck as the opposite side and the horizontal distance to the ship as the adjacent side of a right triangle.
Given that the angle of depression is 67 degrees and the height of the observation deck is 955 feet, we want to find the horizontal distance (adjacent side).
Using the trigonometric function tangent, we can set up the following equation:
tan(67°) = opposite/adjacent
tan(67°) = 955/adjacent
To find the value of the adjacent side (horizontal distance), we can rearrange the equation:
adjacent = 955/tan(67°)
Using a calculator, we can evaluate the tangent of 67 degrees:
tan(67°) ≈ 2.3693
Now we can substitute this value into the equation:
adjacent = 955/2.3693
adjacent ≈ 403.81
Therefore, the horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.
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find the center of the circle that you can circumscribe about triangle ABC. A(2,8) B(0,8) C(2,2)
The center of the circumscribed circle is (1, 5).
How do we calculate?We calculate the midpoint and slope of the line segment AB:
Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)
Midpoint of AB = (1, 8)
Slope of AB = (y₂ - y₁) / (x₂ - x₁)
= (8 - 8) / (0 - 2)
Slope= 0
We can notice that the equation of the perpendicular bisector of AB is x = 1.
We also find midpoint and slope of the line segment BC
Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((0 + 2) / 2, (8 + 2) / 2)
= (1, 5)
Slope of BC = (y₂ - y₁) / (x₂ - x₁)
= (2 - 8) / (2 - 0)
= -3
y - 5 = -3(x - 1)
y - 5 = -3x + 3
3x + y = 8
we have the equations of two perpendicular bisectors which are
x = 1 and 3x + y = 8.
We Substitute x = 1 into 3x + y = 8:
3(1) + y = 8
3 + y = 8
y = 5
In conclusion, center of the circumscribed circle is (1, 5).
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The revenue in dollars of a shoe store is modeled by the expression -4.1x² + 9x + 1,325 where x is the number of shoes sold. The cost of selling the shoes is modeled by the expression -10.1x² - 9.6x +10,000. What simplified expression models the profit in
dollars of the company as a function of x?
The sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.
How to find determine the expression models the profit in dollars of the company as a function of xUsing the formula:
D = 10 * log(I/I0),
where D represents the sound intensity in decibels, I is the given sound intensity, and I0 is the reference intensity of 10^-12 watts per square meter.
Substituting the given values:
D = 10 * log(8.2*10^2 / 10^-12).
To simplify the calculation, we can rewrite the division as multiplication by the reciprocal:
D = 10 * log(8.2*10^2 * 10^12).
Using the logarithm property log(a * b) = log(a) + log(b):
D = 10 * (log(8.2) + log(10^2) + log(10^12)).
Using the logarithm property log(a^b) = b * log(a):
D = 10 * (log(8.2) + 2 * log(10) + 12 * log(10)).
Since log(10) = 1:
D = 10 * (log(8.2) + 2 + 12).
D = 10 * (log(8.2) + 14).
Using a calculator or logarithm table, we can find log(8.2) ≈ 0.913.
D = 10 * (0.913 + 14).
D = 10 * 14.913.
D ≈ 149.13.
Therefore, the sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.
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Need this asap will give brainliest
Answer:
Angles 3 and 5 are consecutive interior angles.
Solve the following equation by Graphing:
0 = x^2 - 6x + 7
Answer:
See below
Step-by-step explanation:
Where the graph crosses the x-axis will solve the equation
Pedro observed what customers ordered at his ice cream shop and found the following probabilities:
�
(
vanilla
)
=
0.3
�
(
sundae
)
=
0.2
�
(
vanilla and sundae
)
=
0.15
P(vanilla)=0.3
P(sundae)=0.2
P(vanilla and sundae)=0.15
Find the probability that a customer ordered vanilla ice cream given they ordered a sundae.
The probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.
To find the probability that a customer ordered vanilla ice cream given they ordered a sundae, we can use the concept of conditional probability.
The conditional probability of an event A given event B is denoted as P(A|B) and is calculated as the probability of both events A and B occurring divided by the probability of event B.
In this case, we want to find P(vanilla|sundae), which represents the probability of a customer ordering vanilla ice cream given that they ordered a sundae.
Using the given probabilities:
P(vanilla) = 0.3
P(sundae) = 0.2
P(vanilla and sundae) = 0.15
The probability of a customer ordering a sundae is the denominator for the conditional probability. Therefore, P(sundae) will be the denominator.
P(vanilla|sundae) = P(vanilla and sundae) / P(sundae)
Substituting the given values:
P(vanilla|sundae) = 0.15 / 0.2
Now we can simplify:
P(vanilla|sundae) = 0.15 / 0.2
= 0.75
Therefore, the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.
In conclusion, based on the given probabilities, there is a 75% chance that a customer who ordered a sundae also ordered vanilla ice cream.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The calculated measure of the angle 1 is 43 degrees
How to determine the measure of the angle 1From the question, we have the following parameters that can be used in our computation:
The circle
Also, we have
The line AB tangent to the circle
This means that
Angle 1 = 1/2 * the arc subtended by the line
So, we have
Angle 1 = 1/2 * 86
Evaluate
Angle 1 = 43
Hence, the measure of the angle 1 is 43 degrees
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Direction: Read each item carefully. Encircle the best answer from the given
choices.
1. What is A U B; if A = {<, +, =, x) and B = {=, +, /, >}
A. {<, +, =, X}
C. {<, +, =, x, /, >}
B. (=, +, /, >}
D. {<, +, =, x, =, +, /, >}
2. What is An M; if A = {1, 2, 4) and M = {2, 3, 5}?
A. {1}
C. (3)
B. (2)
D. (4)
3. What is Bn C; if B = {C, O, U, G, H) and C = {F, E, V, E, R)
C. (F, E, V, E, R}
A. {}
B. (C,O,U,G,H}
D. (C, O, U, G, H, F, E, V, E, R}
4. What is M - J; if M = {soap, alcohol, sanitizer, mask) and J = {alcohol,
sanitizer, mask, gloves}?
A. {alcohol)
C. {mask}
B. (gloves)
D. (soap}
5. What is complement of set A if U = {Frontliners, sacrifice, their, lives, to,
combat, coronavirus) and B = {Frontliners, sacrifice, their, lives)
A. (Frontliners)
C. (to, combat, coronavirus}
1) The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) The value of A ∩ M is,
A ∩ B = {2}
3) The value of B ∩ C is,
B ∩ C = { }
4) The value of M - J is,
M - J = {soap}
5) The complement of set A is,
A' = (to, combat, coronavirus}
Now, WE can simplify as;
1) We have;
A = {<, +, =, x) and B = {=, +, /, >}
Hence, We get;
The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) Given that,
A = {1, 2, 4) and M = {2, 3, 5}
Hence, The value of A ∩ M is,
A ∩ B = {2}
3) Given that;
B = {C, O, U, G, H) and C = {F, E, V, E, R)
Hence, The value of B ∩ C is,
B ∩ C = { }
4) Given that;
M = {soap, alcohol, sanitizer, mask) and J = {alcohol, sanitizer, mask, gloves}
Hence, The value of M - J is,
M - J = {soap}
5) Given that;
U = {Frontliners, sacrifice, their, lives, to, combat, coronavirus) and A = {Frontliners, sacrifice, their, lives)
Hence The complement of set A is,
A' = U - A
A' = (to, combat, coronavirus}
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Need this asap will give brainliest
Answer:
measure of angle 7 + measure of angle 8 = 180°.
Describe the Transformations for 4 and 5
If h(x) = f(–x), this is saying that your graph will be reflected over the y-axis. In other words, the x-values of every point on the graph of y=f(x) will be switched to the opposite sign. The graph will be flipped over sideways.
For example, if (1,-4) is a point on y=f(x), then y=h(x) will have (–1,-4) on it.
If h(x) = –f(x), this is saying that your graph will be reflected over the x-axis. In other words, the y-values of every point on the graph of y=f(x) will be switched to the opposite sign. The graph will be flipped upside-down.
For example, if (1,–4) is a point on y=f(x), then y=h(x) will have (1,4) on it.
While you are given the equation for f(x) in each exercise, the function f(x) does not impact the transformation at all. What is said above is true for all functions.
If you want to graph them, then for 4:
f(x) = -3 - x
h(x) = f(-x) = -3 + x
For #5:
f(x) = 1/3 x + 1
h(x) = -f(x) = -1/3 x - 1
Please help (easy economics question)!!!
The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total revenue will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.
To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:
Price: $[tex]6[/tex]
Quantity: [tex]0[/tex]
Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]
Price: $[tex]5[/tex]
Quantity: [tex]2[/tex]
Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]
Price: $[tex]4[/tex]
Quantity: [tex]3[/tex]
Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]
Price: $[tex]3[/tex]
Quantity: [tex]4[/tex]
Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]
Price: $[tex]2[/tex]
Quantity: [tex]5[/tex]
Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]
Price: $[tex]1[/tex]
Quantity: [tex]6[/tex]
Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]
To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.
Therefore, at a price of $[tex]3[/tex], the total revenue will be the greatest, with [tex]4[/tex] units sold.
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What is the lateral surface area of the triangular prism below?
The lateral surface area of the triangular base prism is 288 m².
How to find the lateral area of a triangular prism?The lateral area of the triangular base prism can be found as follows:
Lateral area of the triangular base prism = (a + b + c)h
where
a, b and c are the side of the triangleh = height of the prismTherefore,
a = 7 m
b = 8 m
c = 9 m
h = 12 m
Therefore,
Lateral area of the triangular base prism = (7 + 8 + 9)12
Lateral area of the triangular base prism = 24 × 12
Lateral area of the triangular base prism = 288 m²
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3.2.3. In the table below, the written explanation of the steps have been provided, show the
mathematical steps for the explanations given.
WH
Factorize x²+x-12
Mathematical steps.
x² + 4x -3x - 12
(x+4)(x-3)
Explanation
Rewrite the middle term of the trinomial
using the values from the chart above.
Group pairs of terms.
Factor out the HCF of the first group.
Factor out the HCF of the second group.
Factor out HCF of the two terms
The final factorized answer
SURINATE
k
9. The table shows the results from a study in which some patients were treated with a new
medical drug for sleeping disorders and others received a common sleeping pill. Use a 0.05
significance level to find the critical value needed to test for independence between the type of
sleeping pill and the presence of any adverse health condition.
Adverse health
condition reported
No adverse health
condition reported
00.004
03.841
00.751
0.100.
New Sleeping Pill Common Sleeping Pill
135
132
145
122
(1 point)
The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.
The null hypothesis in this case would be that there is independence between the type of sleeping pill and the presence of any adverse health condition.
The critical value needed to test for this is the chi-squared statistic with a significance level of 0.05.
To calculate the critical value, we first need to calculate the degrees of freedom, which is calculated by (rows-1) * (columns-1). In this case, the degrees of freedom is (2-1)*(2-1) = 1.
The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. This means that if the calculated chi-squared statistic is greater than 3.84, then we can reject the null hypothesis and claim that there is a significant relationship between the type of sleeping pill and the presence of any adverse health condition.
Therefore, the critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.
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There are thirteen boys and fifteen girls in a class. The teacher randomly selects one student to answer a question. Later, the teacher selects a different student to answer another question. What is the probability that the first student is a boy and the second a girl? Explain.
Step-by-step explanation:
To solve this problem, we need to calculate the probability of the first student being a boy and the second student being a girl.
There are a total of 13 boys and 15 girls in the class, making a total of 28 students.
The probability of the first student being a boy is given by:
P(boy) = Number of boys / Total number of students = 13 / 28
After the first student is selected, there are now 27 students remaining (since one student has already been selected). Out of these 27 students, there are still 15 girls remaining.
The probability of the second student being a girl, given that the first student was a boy, is given by:
P(girl|boy) = Number of girls / Remaining number of students = 15 / 27
To find the probability of both events occurring (the first student being a boy and the second student being a girl), we multiply the individual probabilities:
P(boy and girl) = P(boy) * P(girl|boy) = (13/28) * (15/27)
Calculating this expression:
P(boy and girl) ≈ 0.2041
Therefore, the probability that the first student is a boy and the second student is a girl is approximately 0.2041 or 20.41%.
find the surface area
400Answer:
Step-by-step explanation:
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: Area = = 38.5 - Perimeter - 29.6819.
Step-by-step explanation:
To find the perimeter and area of a triangle with vertices L(5,5), M(-2,-4), and N(5,-6), we can use the distance formula and the formula for the area of a triangle.
Perimeter:
The perimeter of a triangle is the sum of the lengths of its sides. We can find the lengths of each side using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the lengths of LM, MN, and NL:
LM = √((-2 - 5)^2 + (-4 - 5)^2)
= √((-7)^2 + (-9)^2)
= √(49 + 81)
= √130
MN = √((5 - (-2))^2 + (-6 - (-4))^2)
= √((7)^2 + (-2)^2)
= √(49 + 4)
= √53
NL = √((5 - 5)^2 + (-6 - 5)^2)
= √((0)^2 + (-11)^2)
= √(0 + 121)
= √121
= 11
The perimeter of the triangle is the sum of these three sides:
Perimeter = LM + MN + NL
= √130 + √53 + 11 = 29.6819
Area:
To calculate the area of the triangle, we can use the formula for the area of a triangle using the coordinates of its vertices. The formula is given by:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Using the coordinates of L(5,5), M(-2,-4), and N(5,-6), we can calculate the area:
Area = 0.5 * |5(-4 - (-6)) + (-2)(-6 - 5) + 5(5 - (-4))|
= 0.5 * |5(2) + (-2)(-11) + 5(9)|
= 0.5 * |10 + 22 + 45|
= 0.5 * |77|
= 38.5
Therefore, the perimeter of the triangle is given by √130 + √53 + 11 = 29.6819 units, and the area of the triangle is 38.5 square units.
Write the quadratic equation in standard form that corresponds to the graph shown below.
The quadratic equation shown in the graph is:
y = x² + 2x - 8
How to write the quadratic equation?Here we want to find the graph of the given quadratic equation, where we only know the zeros of it.
Remember that if a quadratic equation has the zeros:
x = a
x = b
Then we can write it as:
y = (x - a)*(x - b)
Here the zeros are:
x = -4
x = 2
Then we can write:
y = (x + 4)*(x - 2)
Expanding that we will get the standard form:
y = x² + 4x - 2x - 8
y = x² + 2x - 8
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what is the value of z (2x+6) degrees 12 degrees
The value of x indicated in the right angle of EFG is determined as 36.
option D.
What is the value of x?The value of x is calculated by applying the principle of sum of angles in a right angle triangle as follows;
A right triangle has a right angle and two angles that are complementary.
If angle EFG is a right angle, then the sum of angles at point F is 90 degrees.
The value of x is calculated by setting up the following equations;
2x + 6 + 12 = 90
2x + 18 = 90
2x = 90 - 18
2x = 72
x = 72/2
x = 36
Thus, the value of x is calculated by applying the principle of sum of angles in a right angle triangle.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
[tex]x^2+2y=1[/tex]
Step-by-step explanation:
The equation of a parabola with a vertical axis of symmetry,
focus (h, k+p), and directrix x=h-p is given by:
[tex](x - h)^2 = 4p(y - k)[/tex]
In this case, the focus is (0, 1) and the directrix is x =3.
Comparing this to the general equation,
we have
h = 0, k = 1, and x = h - p = 3.
From x = h - p, we can solve for p:
3 = 0 - p
p = -3
Substituting the values of h, k, and p into the equation, we get:
[tex](x - 0)^2 = 4(-3)(y - 1)[/tex]
Simplifying further:
[tex]x^2 = -12(y - 1)[/tex]
[tex]x^2=-12y+1[/tex]
[tex]x^2+12y=1[/tex]
Therefore, the parabola equation is [tex]x^2+2y=1[/tex]
Use the hundredths grid to answer the question. A 10 by 10 grid is shown. 4 columns and 7 squares are shaded. 2 columns and 5 squares are shaded. Which equation is shown by the shaded area of the model? A. 0 . 29 + 0 . 43 = 0 . 72 B. 0 . 43 + 0 . 22 = 0 . 65 C. 0 . 47 + 0 . 25 = 0 . 72 D. 0 . 23 + 0 . 42 = 0 . 65
Answer:
What the other guy said
Step-by-step explanation:
HELP!!! what is the answer!!!!
Answer:
Step-by-step explanation:
the of of 50 percent of people is married
A rhombus with horizontal
diagonal length 2 centimeters
vertical diagonal length 3 centimeters.
Find the area of the rhombus-shaped keychain.
3 cm2
5 cm2
6 cm2
12 cm2
The area of the Rhombus-shaped keychain is 3 square centimeters.
The area of the rhombus-shaped keychain,
we can use the formula:
Area = (diagonal1 * diagonal2) / 2
Given that the horizontal diagonal has a length of 2 centimeters and
the vertical diagonal has a length of 3 centimeters,
we can substitute these values into the formula:
Area = (2 * 3) / 2
= 6 / 2
= 3 cm^2
Therefore, the area of the rhombus-shaped keychain is 3 square centimeters.
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Which mathematical statement represents "17 more than a number is 26"?
17>26
On+17-26
17<26
O26+n-17
The mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26
Given that a statement we need to convert it into a mathematical statement,
The mathematical statement that represents "17 more than a number n is 26" can be written as:
n + 17 = 26
To solve for n, we can subtract 17 from both sides of the equation:
n + 17 - 17 = 26 - 17
Simplifying the equation gives:
n = 9
Therefore, the number n is 9.
Hence the mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26
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