The length of the longer diagonal of the given rhombus with side length 51units and shorter diagonal 48 units is equal to 90units.
As given in the question,
Side length of the given rhombus 's' = 51 units
Length of the shorter diagonal of given rhombus 'a' = 48 units
Let us consider length of the longer diagonal of the given rhombus be 'b'
As per the property of the rhombus:
Diagonals of the rhombus bisects each other at right angle
Triangle formed by side length bisecting diagonals is right angled triangle.
Using Pythagoras theorem we have,
(Side length)² = (a/2)² + (b/2)²
Substitute the values
⇒ (51)² = (48/2)² + (b/2)²
⇒2601 = 576 + (b/2)²
⇒(b/2)² = 2601 -576
⇒(b/2)² = 2025
⇒b/2 = √2025
⇒ b/2 =45
⇒ b = 90units
Therefore, the length of the longer diagonal of the given rhombus is equal to 90units.
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Extended Response
1. (6) The weights of grapefruits, G, of a certain variety are approximately Normally
distributed with a mean of 1 pound and a standard deviation of 0.12 pounds.
a. Let T = 3G. Find the mean and standard deviation of T.
b. Let R = G+ G + G. Find the mean and standard deviation of R.
c. Let Q=T-R. Find the mean and standard deviation of Q.
The mean and standard deviation of T, the mean and standard deviation of R, and the mean and standard deviation of Q.
0.120.20.2236What is the mean and standard deviation of Q.?a. The mean and standard deviation of 7-G is
7-1=6 and 0.12, respectively.
b. Let X be the weight of a single grapefruit, so the mean and standard deviation of X are 1 and 0.12, respectively.
The mean and standard deviation of R=G+G+G are
3*1=3
and
√(3)*0.12=0.2, respectively.
c. The mean and standard deviation of
Q=T-R are 7-3=4
√0.2((0.12^2)+(0.2^2))=0.2236 respectively.
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On a math fact tet Paul got 1/8 of the quetion incorrect in percent and fraction form how many quetion did Paul get wrong
Fraction form 12.5% question did Paul get wrong .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided.
Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator.
Fraction of incorrect question = 1/8
Present of incorrect question
Computation:
Present of incorrect question = (Fraction of incorrect question)(100)
Present of incorrect question = (1/8)(100)
Present of incorrect question = 12.5%
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What is the equation of a line that is perpendicular to y-3x-2 and passes
through the point (6, 8)?
A. y=-x+10
OB. y--x+8
OC. y-x+6
OD. --x+4
The perpendicular equation is y = -1/3x + 10 Option A
How to find perpendicular of an equation?You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 3 we flip it and make it a negative and the new slope is -1/3.
Now we can use that and the point to get the y intercept using slope intercept form.
y = mx + c
m = gradient of the line
c = y -intercept
8 = (-1/3)(6) + c
8 = -2 + c
10 = c
And now we can use our new slope and new intercept to model the equation. y = -1/3x + 10
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Can anyone help solve for x
Answer:
X = 33.19
Step-by-step explanation:
You're welcome.
a triangle undergoes a dilation with a scale factor of 9/5. the resulting triangle is _[blank]_ the original triangle.
The resulting triangle is 9/5 the original triangle.
How triangle dilated with scale factor?
The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).
According to question:Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 9/5,
Then changed triangle is A'B'C'
So, relation between them is A'B'C' = 9/5(ABC)
Thus, the resulting triangle is 9/5 multiple of triangle ABC.
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Which transformation is modeled by the function?
The transformations of f(x) are (b) horizontally shrunk by a factor of 1/4, vertically stretched by a factor of 5 and then reflected across the x-axis
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
g(x) = -5(4x)²
Mathematically, these equations can be represented as
g(x) = -5f(4x)
The above equations implies that, we have the transformation to be:
The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4The -5 implies that the function f(x) is vertically stretched by a factor of 5 and then reflected across the x-axisHence, the transformed function is (b(
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Which inequality does not belong with the other three? Explain your reasoning
The inequality does not belong with the other three is - 1 ≤ x/1.25.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given,
1. 4x ≥ 12 ⇒ x ≥ 3.
2. - 1 ≤ x/5 ⇒ - 5 ≤ x.
3. 12 > x/1.25 ⇒ x < 15.
4. 2.5x > - 6.4 ⇒ x > - 2.56.
x ≥ 3 and x < 15 is, 3 ≤ x < 15.
- 5 ≤ x and x > - 2.56 here one common region is x > - 2.56 so - 5 ≤ x does not fit.
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About 68% of sixth-grade students will have heights between_____inches and____inches.
Answer: 55.7 inches and 60.3 inches
Step-by-step explanation:
I saw this question before in math class, so I know the answer! Hope you find this helpful!
Exponential functions
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = ax
Where a>0 and a is not equal to 1.
x is any real number.
If the variable is negative, the function is undefined for -1 < x < 1.
Here,
“x” is a variable
“a” is a constant, which is the base of the function.
An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
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Con la finalidad de otorgar los materiales suficientes para un óptimo trabajo de limpieza, se hizo la siguiente pregunta al personal de intendencia, ¿qué utensilio se gasta más?. Acomoda las etiquetas de los utensilios por debajo de las barras según corresponda.
Answer:
D=Trapeador
A=Cubeta
C=Escoba
B=Recogedor
Step-by-step explanation:
activity 2: Time is gold!
Answer:
time is gold ............
Answer:
q1: it arrived at 11:45
q2: 8 hours and 45 minutes
q3: a: 6:59 AM b: 498 minutes
Step-by-step explanation:
q1: 10:30 + 1:15 = 11:45
q2: 0:30 +7:30 +0:45 +8 hours and 45 minutes
q3: a(8:18 + 10:41 PM = 6:59 AM) b(8x60= 480 +18= 489)
Can you please help me find why these are perpendicular
Answer: It is perpendicular because it makes a 90-degree angles
Step-by-step explanation: A perpendicular is when it makes a 90-degree angle or has the same length!
Hello solve this with steps please
Answer: [tex]x^{2} -5x+3\\[/tex]
Step-by-step explanation:
72 = 2³ x 3²
150 = 2 × 3 × 5²
Work out the lowest common
multiple of 72 and 150, giving
your answer in prime factor form.
Answer:
1800
Step-by-step explanation:
You want the least common multiple (LCM) of 72 and 150 given their prime factorizations:
72 = 2³ × 3²150 = 2 × 3 × 5²Least Common MultipleThe LCM is found as follows:
Identify the unique prime factors (2, 3, 5)Identify the highest power of each (3, 2, 2)Raise those factors to those power to get the LCMLCM(72, 150) = 2³ × 3² × 5² = 1800
Linear quadratic systems
The solution of the given system of equations is (-1, 2).
What is system of equations?
A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.
Consider, the given system of equations.
x^2 - x + 3y - 8 = 0 ..(1)
x - y + 3 = 0 ..(2)
From equation (2),
x = y - 3 ..(3)
Plug the value of x in equation (1).
⇒ (y - 3)^2 - (y - 3) + 3y - 8 = 0
y^2 - 6y + 9 - y + 3 +3y - 8 = 0
y^2 - 4y + 4 = 0
y^2 - 2y - 2y + 4 = 0
y(y - 2) - 2(y - 2) = 0
(y - 2)(y - 2) = 0
(y - 2)^2 = 0
y = 2
Now plug y = 2 in equation (3)
x = 2 - 3
x = -1
hence, the solution of the given system of equations is (-1, 2).
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Choose the system with one solution. (Hint: Try graphing each one on your calculator)
A. y = 7
1
y=-2
B. y = 5x + 2 C. y = 5x + 2 D. 2x + 4y = 6
y = 5x
y = -4x + 2
x + 2y = 3
Problem 9
There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answer:
C)117
Step-by-step explanation:
50%=1/2
If you want to figure out how much is left of a half all you do is have to divide the total number of whatever it is, in this case, its roses, by 2.
So now that we know that, let's get started.
234/2=117
Which we know is correct because it's one of your answer choices.
So 117 roses are not red. The other half was.
I hope this helps!!!
A knife cot 3 time the cot of a poon. 9 poon and 12knive cot 82. 80
How much doe one knife cot
One knief costs 5.52 dollars
Let the cost of knief be x dollars and the cost of spoon be y dollars.
A knife costs 3 times the cost of a spoon.
So, we get an equation,
x = 3y ..............(1)
9 spoons and 12 knives cost $82.80
So, we get an equation,
12x + 9y = 82.80 .........(2)
Substitute above value of x in equation (2),
12(3y) + 9y = 82.80
45y = 82.8
y = 1.84
Subatitute above value of y in equation (1),
x = 5.52
Therefore, the cost of knief is 5.52 dollars
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35x+10y help like rn pls
The value of the 35x + 10y is 330.
What is the linear equation?
A linear equation is an equation of a straight line, written in the form y = mx + b. In this equation, m is the slope of the line and b is the y-intercept. Linear equations are used to describe relationships between variables, and they can also be used to solve problems with multiple unknowns. For example, if you know the slope of a line and the y-intercept, you can use a linear equation to calculate the x-intercept. Linear equations can also be used to model real-world situations, such as calculating the cost of a product or the amount of money saved over a period of time.
We have given:
the value of 35x + 10y, When x=8 and y=5.
Using substitution, substitute the given values of x and y.
35x + 10y
35(8) + 10(5)
280 + 50 = 330
Hence, the value of the 35x + 10y is 330.
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Complete Question:
Find the value of 35x+10y, When x=8 and y=5
HELP ASAP PLS!!!
Zachary purchased a computer for $1,400 on a payment plan. Two months after he purchased the computer his balance was $1,100. Four months after he purchased the computer, his balance was $800. What is an equation that models the balance y after x months?
The equation
models the balance y after x months:
Answer:
Zachary pays $150 per month for his computer
Step-by-step explanation:
after 2 months:
2x + 1100y = 1400..... equation 1
after 4 months:
4x + 800y = 1400...... equation 2
we can either multiply equation 1 by 2 or we can divide equation 2 by 2, the purpose is simply to get the x values equal so it can be eliminated from the equation.
dividing equation 2 by 2:
2x + 400y = 700 ...... equation 3
Now equation 1 minus equation 3:
0x + 700y = 700
700y = 700
y = 700/700
y = 1
substituting y=1 into equation 3
2x + 400(1) = 700
2x = 700 - 400
2x = 300
x = 300/2
x= 150
Therefore it is concluded that Zachary has a payment plan where he pays $150 each month for the computer
if
[tex]a \sqrt{2 } + b \sqrt{5 } = 3(2 \sqrt{2} - 3 \sqrt{ {5} } ) \: find \: the \: value \: of \: a[/tex]
please tell the
answer
Answer:
see attached
Step-by-step explanation:
Kathryn runs from the north west corner to the southeast corner of a rugby field and Mia runs from the northeast corner to the southwest corner. Mia says she ran farther
Mia is incorrect, as they both ran the same distance, which is the hypotenuse of a right triangle of dimensions 10m and 16m.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the lengths of the sides squared.
The sides are between the angle of 90º, while the hypotenuse is the segment that connects the sides.
From the image given at the end of the answer, the distances ran from each of them are equal, which is the hypotenuse of a right triangle of dimensions 10 m and 16 m, thus the distance is obtained as follows:
d² = 10² + 16²
d = square root of (10² + 16²)
d = 18.87m.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Given a triangle with a=80, b=51 and c=113, find C
Using cosine law of triangle and using the provided value for the sides, the value of angle C is [tex]118^{o}[/tex] .
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
How does cosine law work?It is especially helpful for filling in the gaps in a triangle's information. The cosine rule, for instance, enables one to determine any of the angle measurements when all three sides of a triangle are known. Similar to this, using the cosine rule, one can determine the length of the third side given two sides and the angle between them are known.
a=80
b=51
c=113
[tex]cos(C) = \frac {a^{2}+b^{2} - c^{2}}{2ab}[/tex]
cos(c)= -0.4617
C= [tex]118^{o}[/tex]
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What is the product of 7x -4 and 8x +8
Answer:
56x-32
Step-by-step explanation:
7x-4 Times 8x+8
7xtimes8x
56x-4times8
56x-32
Find the indicated angle using trigonometry
The measure of indicated angle in the given triangle is 71.035°.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given right angled triangle, hypotenuse side is 74 units and the two legs of triangle are 70 units and 24 units.
Let the unknown angle be x.
We know that, tanθ =Perpendicular/Base
Now, tan x= 70/24
tan x= 2.91
x =71.035°
So, one of the angle in the triangle is 71.035°.
Therefore, the measure of unknown angle is 71.035° in the given triangle.
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Mr. Ramli is a small entrepreneur, he wants to invest RM 2000 in a spice business. He
is confident that his investment, RM y will increase at a rate 2(x+121) which x is time
in year.
Find the number of years it takes for his investment money to be doubled from his
original investment.
Mr. Ramli's investment in the small entrepreneurship will be doubled in 8 year.
Explain the term rate of change?The term "rate of change" (ROC) describes the rate which something evolves over time. Thus, it is not the amount of specific changes themselves but rather the acceleration or slowdown of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.For the stated equation-
rate of increase is given as-
dy/dx = 2(x + 121) < - rate of the change
dy = 2(x + 121)dx
Integrating;
∫dy = ∫2(x + 121)dx
y = x² + 242x + C
At x = 0, y(0) = 0 Thus,
(0)² + 242(0) + C = 2000
C = 2000
Now, y = x² + 242x + 2000
Calculate 't' to get the y(t) = 40,000 (double the amount)
4000 = x² + 242x + 2000
x² + 242x - 2000 = 0
Find the factor;
x = 8 and x = -250
As, x is time in year. So, x = 8 years.
Therefore, it takes eight years for his investment capital to double from what he initially put up.
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joe is a wrestler and during his workouts he loses 2 pounds. how much water would he have to drink to replenish this water weight loss?
Answer:
36 ounces or if over 150 lbs drink more water than 36 ounces
Step-by-step explanation:
For every pound of sweat you lose you need to drink 16 ounces of water!
What are the roots of the equation x² - 12x + 72 = 0 in simplest a + bi form?
Step-by-step explanation:
[tex] {x}^{2} - 12x + 36 = - 36[/tex]
[tex](x - 6) {}^{2} = - 36[/tex]
[tex](x - 6) {}^{} = 6i[/tex]
[tex]x = 6 + 6i[/tex]
[tex]x = 6 - 6i[/tex]
a poll is conducted the day before an election for state senator. there are two candidates running. the poll shows that 53% of the voters surveyed favor the republican candidate, with a margin of error of 2.as percentage points. should the republican be confident that she'll have a victory party? why or why not?
The lower limit of the confidence interval is 51%, which is above 55%, so the Republican should expect to win.
What does confidence interval mean?
Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.
If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. In statistics, confidence is another word for probability.
A confidence interval of proportions has two bounds, a lower bound and an upper bound.
These bounds depend on the sample proportion and the margin of error.
The lower bound is the sample proportion subtracted by the margin of error.
The upper bound is the margin of error added to the sample proportion.
In this problem, we have that:
Sample proportion 53%
Margin of error 2%
53 - 2 = 51%
53 + 2 = 55%
Hence, the lower limit of the confidence interval is 51%, which is above 55%, so the Republican should expect to win.
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pls help due asap!!!!!!!!!!!!!!
Answer:
(0,2)
Step-by-step explanation:
im not too educated with this topic but i believe we multiple x and y by 1/2
0x1/2=0
4x1/2=2
(0,2) is the answer
:)