A rhombus has a perimeter of 88 and


two acute angles that measure 40° each.


Find the length of the shorter diagonal.


PLEASE HELP ME ASAP

Answers

Answer 1

The length of the shorter diagonal is approximately 7.07 units.

A rhombus is a four-sided polygon in which all sides are equal in length. It is also called a diamond shape because it is often used for diamond-shaped figures. In this case, we are given that the perimeter of the rhombus is 88. Since all sides of the rhombus are equal, we can divide the perimeter by 4 to find the length of one side.

88 ÷ 4 = 22

Therefore, each side of the rhombus measures 22 units.

We are also given that two of the angles in the rhombus are acute angles measuring 40° each. Since all angles in a rhombus are equal, we can find the measure of the other two angles by subtracting the sum of the acute angles from 360.

360 - 2(40) = 280

Each of the other two angles measures 140°.

To find the length of the shorter diagonal, we can use the formula:

Shorter diagonal = (2 × Area) / Length of longer diagonal

The area of a rhombus can be found by multiplying the length of the longer diagonal by the length of the shorter diagonal and then dividing by 2.

Area = (diagonal1 × diagonal2) / 2

We know that the longer diagonal is twice the length of the shorter diagonal.

Longer diagonal = 2 × Shorter diagonal

Substituting these values into the formula, we get:

Shorter diagonal = (2 × (22 × Shorter diagonal × sin 40°)) / (2 × Longer diagonal)

Simplifying, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / Longer diagonal

Plugging in the values we know, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / (2 × Shorter diagonal)

Shorter diagonal = 11 × sin 40°

Using a calculator, we can find that:

Shorter diagonal ≈ 7.07

Therefore, the length of the shorter diagonal is approximately 7.07 units.

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Related Questions

Real world linear equation
I just don’t know how to plug it in all the numbers are already there

Real world linear equation I just dont know how to plug it in all the numbers are already there

Answers

Answer: 3 toys

Step-by-step explanation:

Equation: 60-5t=45

Solving: 5t=60-45

5t=15

t=3

Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500. With this average, the company can stay competitive with rates but not lose money. However, the statistician for the company believes that the cost of the average claim has increased. He pulled 40 recent claims and found the average to be $2,350. Which most restrictive level of significance would suggest that the company should raise rates

Answers

Answer:

The answer is 5% because its correct lol

Step-by-step explanation:

The most restrictive level of significance that would suggest the company should raise rates is a p-value less than or equal to 0.01.

What is hypothesis testing?

Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.

It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.

We have,

To determine if the increase in the average cost per claim is statistically significant, we can perform a hypothesis test.

Let's use a one-sample t-test, where:

Null hypothesis (H0): The average cost per claim is still $2,200.

Alternative hypothesis (Ha): The average cost per claim is greater than $2,200.

We can use a t-test because we have a sample mean, sample size, and population standard deviation.

The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (standard deviation/√ (sample size))

Plugging in the values given, we get:

t = (2350 - 2200) / (500 / √(40))

t = 4.38

Using a t-table with degrees of freedom (df) = 39 (sample size - 1), we can find the p-value associated with this test statistic.

At the 0.01 level of significance (most restrictive level), the critical t-value is 2.704.

Since our calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is evidence to suggest that the average cost per claim has increased.

Therefore,

The most restrictive level of significance that would suggest the company should raise rates is a p-value less than or equal to 0.01.

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The number of beads in a jar is 50 to the nearest ten.
(a) What is the minimum possible number of beads in the jar?
(b) What is the maximum possible number of beads in the iar?

Answers

The answers are 45 and 54

In your own words, describe what the word "congruent" means.

Answers

Answer:

heres a sentence using it

Eating five chocolate bars is not congruent with your plan for losing weight.

Triangles are considered congruent when they have the same angles.

it means

having the same size and shape

Answer:

Congruent

Step-by-step explanation:

Multiple objects the work well together.

Hope this helps (:

experimental and quasi-experimental designs are similar in what aspect of the design?

Answers

Experimental and quasi-experimental designs share similarities in terms of their focus on investigating cause-and-effect relationships. These designs both involve manipulating variables and observing their effects on an outcome of interest.

However, they differ in terms of the level of control the researcher has over the assignment of participants to groups. Experimental designs are characterized by the random assignment of participants to different groups or conditions. This randomization helps ensure that any observed differences between groups can be attributed to the manipulation of the independent variable. The researcher has control over the assignment process, allowing for stronger causal inferences. Quasi-experimental designs, on the other hand, lack the random assignment of participants to groups. This may be due to practical or ethical reasons. Instead, participants are assigned to groups based on pre-existing characteristics, such as age or location. While quasi-experimental designs still allow for the examination of cause-and-effect relationships, they are considered less rigorous than experimental designs due to the potential for confounding variables. In summary, experimental and quasi-experimental designs both aim to investigate cause-and-effect relationships. They differ primarily in the level of control the researcher has over participant assignment. Experimental designs use random assignment for greater control, while quasi-experimental designs rely on pre-existing characteristics.

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I need so much help please save me

I need so much help please save me
I need so much help please save me
I need so much help please save me

Answers

Answer:

Step-by-step explanation:

One of the Answers is C

a good way to get a small standard error is to use a ________.

Answers

Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

I need to simplify this trigonometric expression. The answer will be given, but please help me with the process.​

I need to simplify this trigonometric expression. The answer will be given, but please help me with the

Answers

Answer:

Step-by-step explanation:

I've attached a pic, I used y for sin(theta) and x for cos(theta). Shows all steps. See image.

Step 1: use "factoring sum of cubes" to factor the numerator.

Step 2: in the trinomial, in the numerator, rearrange terms to use the sin^2 + cos^2 = 1 .

Step 3: cancel that factor with the denominator.

I need to simplify this trigonometric expression. The answer will be given, but please help me with the

Need help! only have today till I turn in!

Need help! only have today till I turn in!

Answers

Answer:

yes

Step-by-step explanation:

(y1-y2)/(x1-x2)=(10-6)/(8-0) OR (6-10)/(0-8)
= 0.5
In that case you now know. The answer to the first blank (coefficient of x)
To find the y intercept (the second blank), which I will call c, you can use either pair of the coordinates and substitute them in the equation together with the gradient you found previously.
If you choose to sub in (0,6) and since gradient=0.5,
Then: 6=0.5(0) + c
therefore, c=6
Likewise, if you choose to sub in (8,10)
Then: 10=0.5(8) + c
Therefore, c also equals to 6
So in conclusion the gradient of the slop is 0.5 and the y intercept is 6
The linear function will be: y=0.5x + 6

How do I solve this?

How do I solve this?

Answers

Answer:

6/64

Step-by-step explanation:

there's 3 blues and 2 yellows, with 8 total segments.

3/8x2/8=6/64

2. Find the sum, S, for the arithmetic series described? Remember to use the formula

2. Find the sum, S, for the arithmetic series described? Remember to use the formula

Answers

Using the given formula, the sum of S(n) for the arithmetic series is 565.5.

In the given question we have to find the sum S(n) for the arithmetic series

The given formula is S(n)=n/2 {a(1)+a(n)}

The given values are a(1)=12, a(n)=75,n=13

We just have to put values in given formula

S(n)=n/2 {a(1)+a(n)}

S(n)=13/2 (12+75)

S(n)=6.5*87

S(n)=565.5

Hence, the sum of S(n) for the arithmetic series described is 565.5.

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what is 8+4*5+5-9+2+45-12+95463/8+34/2=?

Answers

Answer:

12008.875

Step-by-step explanation:

Just solve for 50 points and brainliest!

10-5+3=

6-4+10=

Answers

Answer:

10-5+3=8

Step-by-step explanation:

6-4+10=12

Answer:

number 1 - 10-5+3=8

number 2 - 6-4+10=12

Marc is planning a party. The hall only rental option is $1,150. , but tha option allows an external caterer to provide the meal. Marc's caterer charges $27. 50 per person. If he plans to invite 50 people, what is a cheap option?

Answers

Answer is The party hall's meal option costs $2,500. The hall-only rental and external caterer option costs $2,525. The party hall's meal option is cheaper.

The circumference of a circle is 16Pi ft.

The radius is ft.

Answers

Answer:

the answer is 8 Pi

Step-by-step explanation:

just divide 16 by 2 because it's half of the diameter

Answer:

The answer is (8)

Step-by-step explanation:

I got it right on edge have a good day.

          ☆*: .。. o(≧▽≦)o .。.:*☆                  

Order of Operations Question
P
E
M
D
A
S

Order of Operations QuestionPEMDAS

Answers

Answer:

c.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

1. Find the dual of each of the following Linear Programs. Hint: Table 4.1 in the book will be helpful. Minimize x
1

−x
2

(b)
s.t. 2x
1

+x
2

−3x
3

=1
3x
1

+2x
2

−x
3

=5

x
1

,x
2

,x
3

unrestricted

Answers

The dual linear program for the given primal linear program is:

Maximize: y1 + 5y2

Subject to:

2y1 + 3y2 ≤ 1

y1 + 2y2 ≤ -1

-3y1 - y2 ≤ 0

y1, y2 unrestricted.

To find the dual of the given linear program, we need to follow these steps:

Step 1: Write the primal linear program in standard form.

Primal Linear Program:

Minimize: x1 - x2

Subject to:

2x1 + x2 - 3x3 = 1

3x1 + 2x2 - x3 = 5

x1, x2, x3 unrestricted

Step 2: Introduce the dual variables.

Let y1 and y2 be the dual variables corresponding to the two constraints in the primal linear program.

Step 3: Write the dual linear program.

Dual Linear Program:

Maximize: y1 + 5y2

Subject to:

2y1 + 3y2 ≤ 1

y1 + 2y2 ≤ -1

-3y1 - y2 ≤ 0

y1, y2 unrestricted

The dual linear program is obtained by switching the objective function from minimization to maximization and reversing the direction of the inequalities in the constraints.

The dual linear program for the given primal linear program is:

Maximize: y1 + 5y2

Subject to:

2y1 + 3y2 ≤ 1

y1 + 2y2 ≤ -1

-3y1 - y2 ≤ 0

y1, y2 unrestricted.

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144 cubic meters in inches.

Answers

Answer:

I think is 8.787e+6 cubic inches.

Can you please answer this question

Can you please answer this question

Answers

Answer:

look above

Step-by-step explanation:

hope it helps

Can you please answer this question

please help me reeeeeeeeee​

please help me reeeeeeeeee

Answers

Answer:

hiiiiiiiii what can i do foe youuui

Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 5.

Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and

Answers

With dilation at center (0,0) and a scale factor of 5, the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

RotationTranslationReflectionDilation or Resizing  

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

The figure's angles are all the same.The midpoints of the figure's sides stay the same as the midpoint of the dilated form.The figure's parallel and perpendicular lines stay the same as the dilated figure's parallel and perpendicular lines.The visuals stay unchanged.

Now,

As we can see from properties that the image does not change in dilation it stays same and angles are also same.

So, we can see coordinates from the given graph

hence,

         the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).

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Daca triunghiul abc ad si be sunt mediane iar ad si be sunt bisectoare atunci triunghiul abc echi

Answers

If in triangle ABC, AD and BE are medians, and AD and BE are also bisectors, then triangle ABC is an equilateral triangle.

In the given scenario, we have triangle ABC with medians AD and BE, which intersect at a point called the centroid. Additionally, it is stated that AD and BE are also bisectors, meaning they divide the angles of the triangle into two equal parts.

First, let's consider the medians AD and BE. Medians divide each side of the triangle into two equal segments, and they intersect at the centroid, which is also the center of gravity of the triangle. The centroid divides each median in a 2:1 ratio, meaning that the distance from the centroid to a vertex is twice the distance from the centroid to the midpoint of the opposite side.

Next, since AD and BE are bisectors, they divide the angles of the triangle into two equal parts. This implies that each angle of the triangle is bisected, resulting in three congruent angles.

By combining the properties of medians and bisectors, we conclude that all three sides of triangle ABC are congruent. Therefore, triangle ABC is an equilateral triangle, where all angles are congruent and all sides have the same length.

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I need help with is one

I need help with is one

Answers

Answer:

Hypotenuse is the longest slanting side

Step-by-step explanation:

Without an angle to consider, the other two could fit in any position

P=PerpendicularB=BaseH=Hypotenuse

Refer to the attachment

I need help with is one

alpha is the probability of committing a type i error TRUE/FALSE

Answers

Answer:

TRUE

Step-by-step explanation:

The probability of committing a type 1 error is called alpha (or the level of statistical significance)

Alpha is the probability of committing a type i error. The statement is True.

Alpha is also known as the level of significance. In hypothesis testing, the level of significance is used to determine the acceptance or rejection of a null hypothesis. It's calculated by dividing the critical value (the value beyond which we can reject the null hypothesis) by the standard deviation of the population. The level of significance is typically set to 0.05 or 0.01. If the p-value (the probability of getting the observed results by chance) is less than the level of significance, we reject the null hypothesis and conclude that the alternative hypothesis is true.

Therefore, it's true that alpha is the probability of committing a type I error, which occurs when we reject a null hypothesis that is actually true. A type I error is also known as a false positive. In other words, we conclude that there is a significant effect or relationship when there isn't one. The level of significance is a measure of how willing we are to make this type of error. If we set a high level of significance, we are more likely to make a type I error.

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Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

24f2+11

Answers

Answer:

24t^2 + 11

Step-by-step explanation:

There is a lot left out of this question. If you are allowed rational numbers, a common factor could be 24.

24(t^2 + 11/24) is one possibility.

I think what you mean is there an integer that is a common factor. There is not.

So the answer is 24t^2 + 11

There is one more thing that needs to be clarified. Can you give t a value? If you can, then t = 11

the common factor would be

11(24 * 11 + 1)

I doubt very much that this is what is meant, but the question really should make it clear.

Answer:

1(24f²+11) is your answer

Step-by-step explanation:

24f2+11

taking common

1(24f²+11)

Find the volume of the cylinder
Either enter an exact answer in terms of t or use 3.14 for t
10
4 units

Answers

Answer:

502.4 cubic unit

Step-by-step explanation:

Given data

The parameter for the cylinder is as follows

Height h= 10units

Radius r= 4 units

We know that the expression for the volume of a cylinder is

V= πr^2h

substitute

V= 3.14*4^2*10

V= 3.14*16*10

V= 502.4 cubic unit

Hence the volume is  502.4 cubic unit

which of the following are the roots of f(x) = 5x4 - 2x3 - 25x2 - 6x 45? (select multiple answers)

Answers

The question is asking for the roots of the polynomial f(x) = 5x4 - 2x3 - 25x2 - 6x + 45. Therefore, the roots of f(x) = 5x4 - 2x3 - 25x2 - 6x + 45 are approximately -1.2 and 1.6.

To find the roots of a polynomial, we need to set f(x) equal to zero and solve for x. This means we are looking for values of x that make the equation f(x) = 0 true. We can do this through factoring or by using numerical methods such as the quadratic formula or Newton's method. To find the roots of f(x) = 5x4 - 2x3 - 25x2 - 6x + 45, we can use various methods. One approach is to try to factor the polynomial.

However, it is not immediately clear how to factor this polynomial, so we can turn to numerical methods. One way to find the roots is to use a graphing calculator or software to plot the function and look for the x-intercepts (where the function crosses the x-axis). This can give us an approximate idea of where the roots are located. Another method is to use iterative numerical techniques such as Newton's method or the bisection method to find the roots with increasing accuracy.


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mary robertson sells tires at a large car service center she earns 10 commission on the first $1000 15 on the next $2000 and 20 on sales of more than $3000 last

Answers

Her total commission was $560.

As 10% of the first $1,000, 15% of the next $2,000, and 20% of sales beyond $3,000 are commissions that she receives. She sold $3,400 worth of tires last week.

What does "total commission" mean?

The commission serves as a benefit or an inducement for the worker to close agreements so that the business can increase revenue and profits. The total commission is calculated by multiplying the total sales by the commission percentage.

After dividing the outcome by 100, multiply the sale price by the commission percentage. Perform the subsequent calculation: Each blue gadget costs $70. The salesman receives a 14% commission on each sale, or $9.80.

The percentage or fixed payment connected to a specific number of sales is referred to as a "commission rate." A commission, for instance, can be $30 or 6% of sales.

It is therefore $560.

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How do you find the scale factor given a center of dilation an image and a Preimage?

Answers

STEPS to find the find the scale factor given a center of dilation an image and a Preimage are given below

What is Scale factor, pre-image and dilation?

Dilation: A dilation is a stretch or a contraction in a figure or point's size and placement.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Scale Factor: In a dilatation, the scale factor refers to how much the figure is enlarged or contracted.

Step 1:

By comparing the length of one side of the pre-image to the corresponding side of the post-image, one may determine the dilation scale factor. The pre-image must be multiplied by the scaling factor to equal the post-image. If the side of the pre-image is the length of \(lpre\)and the length of the corresponding side of the post-image is \(lpost\),

, then the scale factor is given by k in the equation  =  \(lpre\) \(k\)=\(lpost\).

We can solve for k algebraically.

Step 2:-

Choose a matching group of spots on the pre-image and picture. the main point

(x1,y1) being the focal point of the pre-image (x2,y2) be the Centre of the enlarged picture.

By resolving the following two equations, you may get the coordinates of the Centre of dilation,

Step 3:-

Find the coordinate of center of dilation,

\(x_{0}=\frac{kx1 - x2}{k-1} \\\\y_{0}=\frac{ky1 - y2}{k -1}\)

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A. 7/24
B. 24/7
C. 24/25
D. 7/25

A. 7/24 B. 24/7 C. 24/25D. 7/25

Answers

Answer:

d

Step-by-step explanation:

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