The value of x= 35.5, y= 43.75 and z= 62.75
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the three angles are x, y and z.
x+ y + z = 180............(E3)
The sum of the measures of the second and third angles is three times the measure of the first angle.
So, y+ z = 3x
3x- y- z= 0.............(E1)
and, third angle is 19 more than the second
z= y+ 19
y- z= -19..........(E2)
So, E1+E2, and E3-E2,
3x- 2z= -19
x+ 2z= 161
Now, adding above
4x = 142
x= 35.5
and, y + z = 106.5, y- z = -19
Again, adding
2y= 87.5
y= 43.75
and, z= 62.75
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4
If figure ABCD is congruent to MNOP, what
is the length of PM?
6
A
F
H
D 7 C
6789
10
10
8
8
P
N
M
The length of the PM is 6 if ABCD is congruent to MNOP.
What do you mean by congruent?When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.
More specifically, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions including translation, rotation, and reflection. This indicates that either object may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. If we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are then congruent. I'm allowed to turn the paper over.
Here both the given figures are congruent figures. So, their shape and size must be equal.
Therefore from the two figures, PM=DA
So, PM=6
Therefore, the length of the PM is 6 if ABCD is congruent to MNOP.
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please help proportional relationship easy needed now !!
The equations representing the proportional relationships between two variables:
k = 5 · hk = (5 / 4) · hk = (1 / 5) · hWhat are the equations of proportional relationship for each table of values?
In this problem we find three cases of tables showing proportional relationships between two variables. Proportional relationships are represented by equations of the form:
y = k · x
Where:
x - Independent variable.y - Dependent variable.k - Proportionality factor.Each table represents a proportional relationship if and only if each pair of variables has one and same proportionality factor. After a quick inspection, we find the following features:
The first table has a proportionality factor of 5. The equation is k = 5 · h.The second table has a proportionality factor of 5 / 4. The equation of k = (5 / 4) · h.The third table has a proportionality factor of 1 / 5. The equation of k = (1 / 5) · h.To learn more on proportional relationships: https://brainly.com/question/12917806
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helppp me please. i did my points but I need help on the rest
By using linear equation, it can be calculated that
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Equation of line : x + 3y = -3
Putting y = 1
x + 3 [tex]\times[/tex] 1 = -3
x = -3 - 3
x = -6
Putting y = 2
x + 3 [tex]\times[/tex] 2 = -3
x + 6 = -3
x = -3 - 6
x = -9
New solutions (-6, 1) and (-9, 2)
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
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a bag contains 56 marbles, some green and some red. The ratio of green marbles to red ones is 3:4. How many green marbles are there?
15 green marbles are there among 56 marbles.
A bag contains 56 marbles, so Total marbles =56.
In That, There are Green and red marbles contained in a ratio of 3:4.
Now we have to assume that
Let 3x = the number of green marbles and 4x = the number of red marbles
By using the ratios and the total we can know how many green and red marbles are there in a bag. so the formula is:
ax+bx=t-------(1)
a and b are ratios of given marbles
t is the total number of marbles
x is to find the value
substituting the values in the above equation we get
3x + 4x =35
7x = 35
x = 5
substitute the x value in 3x we get:
Green: 3x = 15
Therefore,15 green marbles are present among 56 marbles
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2 A scale model of a building has a height that is 16 inches tall. The actual height of
the building is 240 feet. Which scale is used to represent the scale drawing of the
building?
F 1 inch : 8 feet
G 1 inch 9 feet
H 1 inch 15 feet
J 1 inch 16 feet
Which proportion can be used to find the length of EP in centimeters?
Answer:
inverse proportion
Step-by-step explanation:
2=k240/16
In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
Answer:
Yes it is
Step-by-step explanation:
48.49 ÷ 0.4
Round your answer to the nearest hundredth.
Answer:
121.23
Step-by-step explanation:
48.49/0.4 = 121.225
121.225 rounding into nearest hundredth = 121.23
Complete the inequality for this graph.
y < [?]
Answer: y < 2
Step-by-step explanation:
what does it mean by element c32
Answer:
2 (the first choice)
Step-by-step explanation:
This is a matrix of size 3 rows and 5 columns (3 x 5)
Any element of the matrix can be reference by row and column number
C₃₂ refers to the element in the 3rd row, 2nd column which is 2
In the fall of 1996, tuition and registration fees for undergraduates at the University of California, Davis was $1411. In the fall of 2018, tuition and fees
were $14,402. Find the percent increase. Round your answer to the nearest tenth percent
% increase
To find the percent increase, we need to calculate the difference between the new tuition and fees and the old tuition and fees, and then divide this difference by the old tuition and fees and multiply by 100%.
The difference between the new tuition and fees of $14,402 and the old tuition and fees of $1411 is $14,402 - $1411 = $12,991.
The percent increase is: ($12,991/$1411) * 100% = 9.2 * 100% = 920%
Therefore, the percent increase in tuition and fees between the fall of 1996 and the fall of 2018 was 920%, rounded to the nearest tenth percent.
50 POINTS
Question 5
The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(2 tails).
12.5%
37.5%
50%
75%
Question 6
Which table shows the sample space for spinning the spinner twice?
spinner with 3 equal sections colored yellow, blue, and red
Blue Yellow Red
Red Red Red Red
Blue Blue Blue Blue
Yellow Yellow Yellow Yellow
Blue Yellow Red
Blue Blue, Blue Blue, Yellow Blue, Red
Blue Blue, Blue Blue, Yellow Blue, Red
Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Red, Yellow Blue, Yellow
Yellow Yellow, Red Yellow, Blue Yellow, Blue
Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Blue, Blue Yellow, Blue
Yellow Red, Yellow Blue, Yellow Yellow, Yellow
Question 7
A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(D, D) if two cards are randomly selected with replacement.
one third
two thirds
two sixths
four ninths
This is the question in the picture
The inequality for the value of y can be given as -1/8 < -2/3y, where y < 3/16.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Let the required number is y.
To find the inequality that represents the -1/8 is less than the product of -2/3 and number y.
The product of -2/3 and y = -2/3y
The inequality for the y can be written as,
-1/8 < -2/3y
Solve for the value of y,
1/8 > 2/3 y
3/16 > y
Or y < 3 / 16
The required inequality is -1/8 < -2/3y, where y < 3/16.
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At the end of a snowstorm, Gabriella had 11 inches of snow on her lawn. The
temperature then increased and the snow began to melt at a constant rate of 0.5
inches per hour. Assuming no more snow was falling, how much snow would
Gabriella have on her lawn 3 hours after the snow began to melt? How much snow
would Gabriella have on her lawn after t hours of snow melting?
The snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t
What is a constant rate of change?
A rate of change is a rate that describes how one quantity changes in relation to another quantity.
Constant rate is also called uniform rate which involves something traveling at a fixed and steady pace or else moving at some average speed.
The snow started melting at a rate of 0.5 inches per hour and it is known that 3 hours after the storm ended, the depth of snow was down to 11 inches.
Snow melted in 3 hours = 0.5 * 3 = 1.5 inches
Thus;
The Initial depth of snow = 11 + 1.5 inches = 12.5 inches.
Now, depth of snow on Gabriella's lawn = Initial depth - 0.5(Number of hours)
Let S(t) be the depth of snow on Gabriella's lawn, in inches, t hours after the snow stopped falling.
Hence, the snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t
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It says my answer is correct over a part of the domain of the integrand, but undefined on another part of the domain. Entered Answer 3*In(\n(7*x))+C
Preview Message 3 ln(ln(7x)) +C
Your answer is correct over part of the domain of the integrand, but is undefined on another part of the domain Evaluate the indefinite integral: 1 x In (18) 3 dx x In(7x) = 3*ln[In(7x)]+C
Answer:
3 ln(abs ln(7x)) +C
Step-by-step explanation:
Do not forget to add the absolute value!
Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 95% confidence. Assume that s = 13 based on earlier studies.
The sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 95% confidence. Assume that s = 13 based on earlier studies is 40.58.
How to find the sample size?Making use of the given data to determine the sample size.
Sample size (n) =?
The confidence level = 95% or 0.95
Z-score for 95% confidence interval =1.960
Using this formula
Margin of error = Zα/2 × α/√n
Solving for n
4 = 1.960 × 13/√n
√n = 6.37
n = 40.58
Therefore the sample size is 40.58.
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1. What is the decay factor?
From 2000 to 2013, the value of the U.S. dollar was shrinking. The value of the U.S. dollar
over time v(t) can be modeled by the following formula:
1.36(0.9758)', where t is the number of years since 2000.
0.9758 is the decay factor of the model
How to determine the decay factor?Given that:
The value of the U.S. dollar over time v(t) can be modeled by the following formula:
v(t) = 1.36(0.9758)^t , where t is the number of years since 2000
The form of the exponential decay models is f(t) = ab^t
where,
a is the initial value, b is the decay factor and t is the time
Comparing f(t) = ab^t with v(t) = 1.36(0.9758)^t :
a = 1.36
b = 0.9758
Therefore, the decay factor is 0.9758
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[tex]\sqrt{2x-6 =x-3\\[/tex]
The value of x in the quadratic equation using mathematical operations is 4±√19
What are Quadratic EquationsTo solve this problem, we have to use some mathematical operations to find the value of x.
In this process, we have to remove the square root and solve for x. This will eventually result to a quadratic equation
In the equation given;
√(2x - 6) = x - 3
Square both sides
(√(2x - 6)² = (x - 3)²
This will eliminate the square root
2x - 6 = (x - 3)²
Open the bracket on the right hand side
2x - 6 = x² - 6x - 9
Collect like terms
x² - 6x - 9 - 2x + 6 = 0
x² - 8x - 3 = 0
Solving for x
x = 4±√19
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What is the degree form for 4/ 9 ?
Answer:
the expression is constant, which means it can be rewritten with a factor of x⁰.
The degree is the largest exponent on the variable.
0
1/3 + 2/3
Please help! This is due tomorrow and I need it now
Answer: 1
Step-by-step explanation:
Answer:
1 or 3/3
Step-by-step explanation:
There is a common denominator (bottom number) so you add straight across.
1+2=3 so it is 3/3, which is a whole, making it 1.
The height y (in feet) of an arrow t seconds after it is shot from a bow can be modeled by the function y=-16t² + 112t + 2.
a. Write the function in vertex form.
Y
b. Find the maximum height of the arrow.
The maximum height of the arrow is
feet.
c. How long does it take the arrow to hit the ground? Round your answer to the nearest second.
It takes about seconds for the arrow to hit the ground.
a) The function in vertex form is; y = -16(x - 3.5)² + 198
b) The maximum height if the arrow is; 198 feet
c) The time that it takes the arrow to hit the ground is; 16 seconds
How to write the quadratic equation in vertex form?We are given the function as;
y = -16t² + 112t + 2.
where;
y is the height (in feet) of an arrow
t is the time in seconds after it is shot from a bow
This is the equation of a vertical parabola open downward
The vertex is a maximum
The general form of a quadratic equation in vertex form is;
y = a(x - h)² + k²
where (h, k) is the vertex coordinate
a) y = -16t² + 112t + 2
This is in standard form and using completing the square, we can write in vertex form as;
y = -16(x - 3.5)² + 198
b) The vertex is the point (3.5, 198)
The maximum height of the arrow represents the y-coordinate of the vertex of the function
Thus, the maximum height of the arrow is 198 feet
c) We know that when the arrow hits the ground, the value of y is equal to zero. Thus, at y= 0, we have;
-16(x - 3.5)² + 198 = 0
Rearranging gives;
(x - 3.5)² = (198/16)
(x - 3.5) = ±√(198/16)
(x - 3.5) = ±12.375
x = 12.375 + 3.5
x = 15.875 ≈ 16 seconds which is the time it will take to hit the ground.
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the equation of the normal to the 2x² + 2y² -4x +4y =12 at the point (-1,1) is
To find the equation of the normal to the given curve at the point (-1,1), you can use the following steps:
Rewrite the given equation in the form "y = mx + b," where m is the slope of the curve and b is the y-intercept.
Find the slope of the curve at the point (-1,1). This can be done by taking the derivative of the equation and evaluating it at x = -1.
The slope of the normal line at the point (-1,1) is the negative reciprocal of the slope of the curve at that point. Calculate this value.
Use the point-slope formula to write the equation of the normal line in the form "y - y1 = m(x - x1)," where (x1, y1) is the point (-1,1) and m is the slope of the normal line.
Substitute the values for x1, y1, and m into the point-slope formula to obtain the final equation of the normal line.
For example, if the given equation is 2x^2 + 2y^2 - 4x + 4y = 12, you can follow these steps:
Rewriting the equation in slope-intercept form, we get: y = -x + 2
Taking the derivative of the equation, we get: y' = -1
The slope of the normal line is the negative reciprocal of the slope of the curve, which is 1/-1 = -1
Using the point-slope formula, we get: y - 1 = -1(x + 1)
Substituting the values into the point-slope formula, we get: y - 1 = -1x - 1
Thus, the equation of the normal line at the point (-1,1) is y - 1 = -1x - 1.
For the figure below, suppose
∠3 = 30°
and
∠7 = 97°.
Find the measures (in degrees) of the other angles.
∠1 =
°
∠2 =
°
∠4 =
°
∠5 =
°
∠6 =
°
∠8 =
°
[tex]\angle 1=150^{\circ}[/tex] (linear pair)
[tex]\angle 2=30^{\circ}[/tex] (vertical angles)
[tex]\angle 4=150^{\circ}[/tex] (linear pair)
[tex]\angle 5=83^{\circ}[/tex] (linear pair)
[tex]\angle 6=97^{\circ}[/tex] (vertical angles)
[tex]\angle 8=83^{\circ}[/tex] (linear pair)
Rewrite 1 1/5 using fifths
1 1/5 - 1/3
= __ /__ - 1/3
The value of mixed fraction 1(1/5) using fifths is 6/5.
How may a number be written as a mixed number?
Divide the numerator by the denominator in step 1.The quotient should be expressed as a whole number in step 2. Input the numerator and denominator as the remainder and the divisor, respectively in step 3.As an illustration, we convert 7/3 into a mixed fraction form by using the instructions provided.
[tex]1\frac{1}{5}[/tex] = [(5 * 1) + 1]/5
= (5 + 1) / 5
= 6/5
Hence, The value of mixed fraction 1(1/5) using fifths is 6/5.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer:
False
A sphere is 3 dimensional.
3.
The angles of a triangle are 120°, (x + 16)°, and x°.
What is the value of x?
Pls explain how you get the answer
The triangle has a value of x=22°.
What is a triangle?The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles.
Having three sides, a triangle is a form. Each kind of triangle has a unique name. The size of the angles and side lengths determine what kind of triangle it is (corners). Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.
The sum of all the angles in a triangle must be °
120° + (x+16)° + x° = 180°
2x + 136° = 180°
2x = 180° - 136°
2x° = 44°
x = 22°
The triangle has a value of x=22°.
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For each of the following equations, solve for the variable. If there are multiple solutions, separate them by a comma.
Answers should be integers, fractions, radicals, or in exponential form. No decimals!
1/7㏒ (x-1) + 3㏒ (2)
x=______
3㏑(ω+6) = 5㏑ (6)
ω=____
The solutions to the x and w variables are x = 2097153 and w = (6)⁻²/⁵
How to determine the solution to the variables?From the question, we have the following parameters that can be used in our computation:
1/7log(x - 1) = 3log(2)
3 ln(w + 6) = 5 ln(6)
Solving the equation (1), we have the following equation
1/7log(x - 1) = 3log(2)
Multiply both sides of the equation by 7
So, we have the following representation
log(x - 1) = 21log(2)
Apply the power rule of logarithm
log(x - 1) = log(2)²¹
By comparison, we have
x - 1 = (2)²¹
Evaluate the exponent
x - 1 = 2097152
So, we have
x = 2097153
Solving the equation (2), we have the following equation
3 ln(w + 6) = 5 ln(6)
Multiply both sides of the equation by 1/3
So, we have the following representation
ln(w + 6) = 5/3 ln(6)
Apply the power rule of logarithm
ln(w + 6) = ln(6)³/⁵
By comparison, we have
w + 6 = (6)³/⁵
So, we have
w = (6)⁻²/⁵
Hence, the solutions are x = 2097153 and w = (6)⁻²/⁵
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If a polynomial f(x) has a remainder of 4 when divided by x-5, what is f(5)?
The remainder of 4 when f(x) is divided by x - 5 means that f(5) = 4
How to determine the remainder of the quotientFrom the question, we have the following parameters that can be used in our computation:
The function is given as
Polynomial = f(x)
Remainder = 4
The function is represented as
z(x)
This means that
x = 5 in f(x)
So, we add -5 to both sides of the equation
This gives
x - 5 = 0
Also, we have
A remainder of 4 when divided by x-5
So, when the equation in interpreted, it means
The remainder when f(x) is divided by x - 5 is 4
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What is the value of x in the equation 2/3 (1/2×+ 12) = 1/2(1/3x +14) - 32
Answer:
Step-by-step explanation:
x = 174
A local company offers you an opportunity to sell discount cards. You will have to pay the company a one-time setup fee of $320. Each card will cost you $6. How many cards would you have to sell before your average total cost per card falls to $10?
Answer:
80 cards would have to sold before your average total cost per card falls to $10
Step-by-step explanation:
To find the number of cards you would have to sell to bring the average total cost per card down to $10, you can use the following formula:
number of cards = setup fee / (average total cost per card - cost per card)
Plugging in the values given in the problem, we get:
number of cards = $320 / ($10 - $6)
Solving this equation gives us:
number of cards = $320 / $4
Dividing 320 by 4 gives us a result of 80, so you would have to sell 80 cards before your average total cost per card falls to $10
Another approach is setting it up as y = mx+b
$10 = (320 + 6x) / x
Where x is the number of cards that you need to sell.
Solving for x, we get:
$10x = 320 + 6x
4x = 320
x = 80
y=3x-34
у = 2x — 5
Help me with this
Answer:
x=29 and y=53
Step-by-step explanation:
let y=3x-34 be the first equation (1) and y=2x-5 be the second equation (2)
Using the elimation method, (1)-(2): 0=x-29
-x=-29
x=29
Substitute x=29 into (2),
y=2(29)-5
y=58-5
y=53
So, x=29 and y=53