Triangle VWX is formed by connecting the midpoints of the side of triangle STU.
The lengths of the sides of triangle VWX are shown. What is the length of SU?
Figures not necessarily drawn to scale.
Answers
The length of the side SU will be equal to 4√2.
What is a Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The formula for the Pythagorean theorem will be given as:-
H² = P² + B²
Here,
H = Hypotenuse
P = perpendicular
B= Base
The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.
Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.
H² = P² + B²
sx² = xv² + sv²
sx = √ ( 2² + 2² )
sx = √8
sx = √ ( 2 x 2 x 2 )
sx = 2√2
SU = 2 sx
SU = 2 x 2√2
SU = 4√2
Therefore, the length of the side SU will be equal to 4√2.
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Related Questions
according to the national retail federation, 34% of taxpayers used computer software to do their taxes. a sample of 125 taxpayers was selected. 4. what is the distribution of the sample proportion of the 125 taxpayers that used the computer software to do their taxes? a. n(0.34, 0.0424) b. n(0.34, 82.5) 5. what is the probability that between 28% and 40% of the taxpayers from the sample of 125 used computer software to do their taxes? a. pnorm(0.4,0.34,0.0424)-pnorm(0.28,0.34,0.0424) b. pnorm(0.4,0.34,125)- pnorm(0.28,0.34,125)
Answers
4) the distribution of the sample proportion of the 125 taxpayers that used the computer software to do their taxes is n(0.34, 0.0424) - option A
5) the probability that between 28% and 40% of the taxpayers from the sample of 125 used computer software to do their taxes is pnorm(0.4,0.34,0.0424) - pnorm(0.28,0.34,0.0424) - Option A
4) Given data:
P = 0.34 and n = 125
Since, np = 0.34 * 125 = 42.5 > 10
& n(1 - p) = 125 * 0.66 = 82.5 > 10
Therefore, the normal distribution can be used here:
Mean is μp = p = 0.34
The standard Deviation is σp = [tex]\sqrt \frac{P(1-p)}{n} = \sqrt\frac{(0.34)(0.66)}{125} = 0.0424[/tex]
The distribution of sample proportion will be;
N (0.34, 0.0424)
Therefore, option (a) is correct that is n(0.34, 0.0424)
5) The likelihood that between 28% and 40% of the 125 taxpayers in the sample used tax preparation software is calculated as follows:
pnorm (0.4, 0.34. 0.0424) - pnorm (0.28, 0.34, 0.0424)
Therefore, option A is correct that is pnorm(0.4,0.34,0.0424)-pnorm(0.28,0.34,0.0424)
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Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
Answers
Answer:
c. ∠MPN
Step-by-step explanation:
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, ∠MPN is supplementary to ∠NPI.
How many ways are there to split 12 people into 4 groups with 3 people in each group?
Answers
Please fully explain how to answer number 5 Thank you
Answers
Given: A right triangle with dimensions as shown in the figure
To Determine: The ratio for sin A and cos A
Solution
Given a right triangle ABC with a reference angle A, the trigonometry ratio is
[tex]\begin{gathered} sinA=\frac{opposite}{hypothenuse} \\ cosA=\frac{adjacent}{hypothenuse} \\ tanA=\frac{opposite}{adjacent} \end{gathered}[/tex]From the given right triangle with reference angle A, the hypothenuse is the side facing the right angle. The side facing angle A is the opposite, and the other side is adjacent. This is as shown below
Hence
[tex]\begin{gathered} sinA=\frac{24}{26} \\ cosA=\frac{10}{26} \end{gathered}[/tex]OPTION A is the correct option
Harry invests £6000 in a savings account.
The account pays 3.4% compound interest per year.
Work out the value of his investment after 3
Give your answer to the nearest penny.
years.
Answers
Answer:
$6633.04
Step-by-step explanation:
6000x1.034^3=6633.04
The value of his investment after 3 years will be $6633.04.
What is compound interest?In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
Compound interest is the interest added to the principal amount of a loan or deposit, also known as interest on interest plus interest.
Given that Harry invests £6000 in a savings account. The account pays 3.4% compound interest per year.
The compound interest will be calculated as,
[tex]A = P( 1 + \dfrac{r}{100})^{nt[/tex]
Substitute the values in the equation above and solve,
A = 6000 x 1.034³
A = $6633.04
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At a local print shop, 20 copies can be made for $8. At this rate, how how many copies could be made for $14?
Answers
The number of copies that can be made would be: 35 copies
How to solve for the copies that can be madeWe would have to solve this problem through the use of cross multiplication
such that we have 20 copies = 8 dollars
unknown copies ? = 14 dollars
This can be re written to be arranged in the form
20 = 8 dollars
? = 14 dollars
we would have to cross multiply
14 x 20 = 8 x ?
280 = 8?
divide through by 14
? = 280 / 14
= 20
Hence the copies that would be made is 35 copies for 14 dollars at the local print shop
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What is the equation of the line that passes through the point (-6,-3) and has a slope of 0?
Answers
Step-by-step explanation:
The equation for point-slope form of the equation is:
y - y1 = m(x-x1)
where m is the slope of the line and (x1,y1) is a point on the line.
you fill in the values for m(0), x1(-6), and y1(-3)
y+3=0(x-3) [This is the point-slope form of the equation of this line.]
y+3=0+0
y=0-3
often, y=0-3 will change to y=-3 (this will be the slope-intercept form)
Can u please help me with this answer
Answers
Answer:
option a as x=8 hope you understand my writing , if got some problem comment down
I need help with number 12. you have to spligy the expression and the answer will reveal a letter
Answers
8+9x+4(11-2x)
As a first step we are going to use distributive property of multiplication:
8+9x+44-8x
Solving ths:
52+x
Answer would be M
Which number sentence is true? A. |10| < 1.0 B. |0| = 0 C. |-47| < |-30| D. |-100| < |0|
Answers
The second option (B) that is I0I = 0 is true.
This is a question of modulus.
Let us check all the options to find which one is true.
Let us check for A.
A. I10I < 0
We know that,
I10I = 10 > 0
Hence, this option is false.
Let us check for B.
B. I0I < 0
We know that,
I0I = 0 = 0
Hence, this option is true.
C. I-47I < I-30I
We know that,
I-47I = 47 and I-30I = 30
47 > 30
Hence,
I-47I > I-30I
Hence, this option is false.
D. I-100I < I0I
We know that,
I-100I = 100 and I0I = 0
100 >0
Hence,
I-100I > I0I
Hence, this option is false.
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3x-1 times 3=5 times x+1
Find x
Answers
Answer:
x = -2
Step-by-step explanation:
3x - 1 × 3 = 5 × x + 1
3x - 3 = 5x + 1
3x - 5x = 1 + 3
-2x = 4
-2x/-2 = 4/-2
x = -2
x is equal to -2
Use square roots to solve the equation x2 = –64 over the complex .numbers. Select any solutions that apply.
an 8i
b -8
c -8i^2
d -8i
Answers
[tex]x^2=-64\implies x=\sqrt{-64}\implies x=\sqrt{-1\cdot 64}\implies x=\sqrt{-1}\cdot \sqrt{64} \\\\\\ x=\sqrt{-1}\cdot 8\implies x=i\cdot 8\implies x=8i[/tex]
Low flow showerheads use 2 1/2 gallons of water per minute. If family members shower a total of 2 1/3 hours per week, how much water does the family use for showers each week? Write an expression that represents the problem. Then solve the problem.
Answers
The expression that represents the situation is 5/2(x) and the family uses 350 gallons of water for each week.
Showerheads:
The showerhead is a bathroom fixture that directs the flow of water in a bathroom shower.
Given,
Low flow showerheads use 2 1/2 gallons of water per minute.
And the family uses 2 1/3 hours per week.
Here we need to find the expression for this situation and we also need to find the amount of water used by the family.
First, we have to convert the mixed fraction into improper fraction, then we get,
2 1/2 =5/2
So, for one minute the showerhead use 5/2 gallon of water.
So, the expression for this situation is,
=> 5/2(x).
Where x represents the amount of time in minutes.
Now, we know that the family uses the showerhead for 2 1/3 hours per week.
So, we have to convert this mixed fraction into improper fraction,
2 1/3 = 7/3
We know that, 1 hour = 60 minutes.
So, 7/3 hours is equal to,
=> 7/3 x 60 = 7 x 20 = 140
Then, the amount of water used by the family is,
=> 5/2 (140)
=> 5 x 70
=> 350
Therefore, the amount of water used by the family is 350 gallons per week.
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Mind doing this too?
Answers
The expression that represents the perimeter and area of the rectangle are 10x + 4 and 6x²- 24.
How to find the area and perimeter of a rectangle?The rectangle is a quadrilateral with opposite sides equal to each other.
Opposite sides of a rectangle is also parallel to each other.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = side lengthw = widthTherefore,
l = 3x + 6
w = 2x - 4
Hence,
perimeter of a rectangle = 2(3x + 6 + 2x - 4)
perimeter of a rectangle = 2(5x + 2)
perimeter of a rectangle = 10x + 4
Let's find the expression that represent the area of the rectangle.
Hence,
area of a rectangle = lw
area of a rectangle = (3x + 6)(2x - 4)
area of a rectangle = 6x² - 12x + 12x - 24
Therefore,
area of a rectangle = 6x²- 24
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I'm stuck with this word problem pls helped me
Answers
One of the many branches of mathematics is algebra, which is derived from the Arabic word al-jabr, which means "reunion of fractured pieces, bonesetting."Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.
Solve the problem?
The world's best mathematicians have been baffled by a mathematical problem for decades.The Diophantine equation x3+y3+z3=k, where k is the sum of all the numbers from 1 to 100, is also referred to as the "sum of three cubes. The following will teach you how to identify the problem before moving on to any of the other four steps in the five-step process for solving algebraic problems.Determine the issue.Describe your knowledge.Plan beforehand.Execute the plan.Check to see if the response makes sense.
16x+12y=744
= 16x+12y=744
16x= 744-12y
divide both sides by 16
16x/16=744-12y/16
x= 744-12y/16
744-12y by 16
x =-3y/4+93/2
solving y
16x+12y=744
12y =744-16x
divide by 12
12y/12 =744-16x/12
y= 744-16x/12
y=-4x/3+62
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Find the slope between these two points:
(12, -18), (-15, -18)
Answers
Answer:
The slope is 0.
Step-by-step explanation:
Using the slope formula which is m= y2 - y1 / x2 - x1, plug in the x values and y values of the two points. (12,-18) is x1 and y1. (-15,-18) is x2 and y2.
When plugging it in we get -18 - (-18)/ -15 - 12. You cannot subtract a negative so it turns from subtraction to addition. So, -18 + 18 / -15 - 12 which equals 0/-27. 0 divided by any number is 0. So the slope is 0, m=0.
Hope this helps :)
Steve stopped for a drink of water when he had completed 60% of his jog. He had traveled 3 miles. What is the total distance Steve jogged?
2 miles
3 miles
4 miles
5 miles
6 miles
Answers
The total distance Steve jogged is 5 miles.
what is percent?The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Given:
Steve completed 60% of the Jog.
Also, he travelled 3 miles.
Let the total distance he travelled be x miles.
Then,
60% of x =3
60/100 x= 3
x= 3 x 100 / 60
x= 300/60
x= 5 miles.
Hence, total he had to jog 5 miles.
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(6) If the store likes to keep 30 tiles in stock at all times how many bundles do they need to order now, after selling the 150 tiles to the customer? Think about how many you had left over from the customer when ordered 150 tiles.
Answers
function:
number of tiles: 12b+38
Where;
b=number of bundles
150+30 = 12b+38
Solve for b:
150+30 = 12b+38
180 = 12b+38
180-38 =12b
142 =12b
142/12 =b
11.8 =b
12 bundles
Point F is located at (-6, -2) on the coordinate plane. Point Fis reflected over the
y-axis to create point F'. What ordered pair describes the location of F'?l
Answers
The ordered pair describes the location of F' is (6, -2) reflected over the
y-axis.
What is meant by the term reflection?A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure has been equidistant from every point in another figure. The reflected image should be the same shape and size as the original, but it should face in the opposite direction. Translation can also occur as a result of changes in position.The Y-coordinates of a point remain constant when it is reflected across the Y-axis. However, the X-coordinates are transformed into their inverse signs.
As a result, the Y-axis reflection of a point (x, y) is (-x, y).
For the given question;
Point F (-6, -2) is reflected along the y-axis to form a point F'.
The coordinates of F' becomes (6, -2), negative x axis will becomes positive.
Thus, the ordered pair describes the location of F' is (6, -2) reflected over the
y-axis.
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Translate the sentence into an inequality. A number b increased by 6 is less than or equal to -23. please help asap its due tomr
Answers
Answer: b+6 (less or equal to sign) -23
Step-by-step explanation: b increased by 6 is b+6
Answer: b+6[tex]\leq[/tex]-23 b[tex]\leq[/tex]-29
Step-by-step explanation:
A deck of cards was shuffled and after each shuffle, the suit of the top card was recorded. The table shows theprobability of each outcome. What is the probability that the top card is not a heart?
Answers
Answer:
[tex]0.72[/tex]Explanation:
Here, we want to get the probability that the top card is not a heart card
Mathematically, the sum of the probability that an event will occur and that the event will not occur is 1
Let the event that a heart card is the top card be H
[tex]P(H)\text{ + P(H') = 1}[/tex]We already have P(H) as 0.28
Thus:
[tex]\begin{gathered} 0.28\text{ + P(H') = 1} \\ P(H^{\prime})\text{ = 1-0.28} \\ P(H^{\prime})\text{ = 0.72} \end{gathered}[/tex]1) Define the variable you are using
2) Set up an equation to solve
3) Show all steps of solving the equation
5) Explain what your answer means in terms of the problem.
The number of cupcakes Chad can eat is 2 times the amount his sister can eat. On Chad’s
birthday Chad and his sister ate a total of 12 cupcakes? How many did Chad eat?
Answers
The number of cupcakes that Chad are is 8 cupcakes.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of cupcakes that Chad can buy be x.
The number of cupcakes Chad can eat is 2 times the amount his sister can eat. This will be 2x.
Therefore, the appropriate equation will be:
2x + x = 12
3x = 12
Divide
x = 12/3
x = 4
Chad = 2x = 2 × 4 = 8 cupcakes
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Chocolate milk Riley mix five scoops of chocolate powder with 3 cups of milk Brooke mixes 6 cups of chocolate powder with 4 cups of milk whose mixture is more chocolatey explain how you know
Answers
This mixture has an extra scoop of chocolate ice cream so will taste more chocolatey than 3 scoops of chocolate ice cream and 2 cups of milk.
I’d appreciate the help this is my last few questions and this will save my grade since the first trimester of my school is done this week so I appreciate help
Answers
Answer:
260.52cm^
Step-by-step explanation:
Jessy is looking to subscribe to seventeen magazine for fashion inspiration. Before registering Jessy wants to make sure this is within her budget. Jessy knows there is an initial sign-up fee and a monthly payment required for the subscription. If the monthly subscription fee is $10 and Jessy remembers having a ball on the 2nd month for $26 write an equation that represents the total cost of subscribing to seventeen magazine.
Answers
F - subscription fee
B - Ball on 2nd month
C - seventeen magazine total cost
10f + 26b = c
2 What is the slope of the line in the picture below?
Answers
Explanation
if you know 2 points of a line you can easily find the slope using
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(-1,5)
P2(7,1)
replace,
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{1-5}{7-(-1)} \\ \text{slope}=\frac{-4}{7+1}=-\frac{4}{8}=-\frac{1}{2} \\ \text{slope}=-\frac{1}{2} \end{gathered}[/tex]I hope this helps you
Triangle X has two angles that measure 80° and 30°. Triangle Y has two angles
that measure 80° and 70°. Hannah says that triangles X and Y are not similar.
Jasmine says they are similar. Who is correct? Explain. HELPPP PLEASE
Answers
Answer:
Jasmine is correct. The triangles are similar.
Step-by-step explanation:
Triangle that have the same angle measurements are similar.
The sum of the interior angles of a triangle add up to 180
Triangle x has angles that measure 80 and 30. That totals 110. The third angle must be 70 so that it adds up to 180.
Triangle Y has angels that measure 80 and 70. That adds up to 150, that means that its third angles must be 30
Both triangles have angle measurements to 80, 70, and 30 so they are similar.
HELP MEE((((((((
solve an equation and draw a graph on it
I give 20 points!! please help as soon as possible(
Answers
Hope this helps you. :)
if a number decreases by 8, the result is -21.What is the number?
Answers
Answer: it would be -13
Step-by-step explanation: -13-8=-21
What four consecutive integers have a sum of 86. Name them
Answers
The four consecutive integers are 20, 21, 22, and 23 whose sum is 86.
What do you mean by integer no?using sequential means.
Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.
86 is obtained by adding together the four consecutive integers x, (x+1), (x+2), and (x+3)
x + (x+1), (x+2), and (x+3) = 86
the smallest one, x, is now solved for: 4x + 6 = 86
The numbers are 20, 21, 22, and 23, because 4x = 80 x = 20.
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Answer:
20, 21, 22 & 23
Step-by-step explanation:
Forming the equation,
→ x + (x + 1) + (x + 2) + (x + 3) = 86
→ 4x + 6 = 86
Now the the value of x will be,
→ 4x + 6 = 86
→ 4x = 86 - 6
→ x = 80/4
→ [ x = 20 ]
Then the required numbers will be,
→ x = 20
→ x + 1 = 20 + 1 = 21
→ x + 2 = 20 + 2 = 22
→ x + 3 = 20 + 3 = 23
Hence, numbers are 20, 21, 22, 23.