Considering the triangle with exterior angles and interior angles as described. The statements that are true include
m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°How to determine the statements that are correctThe problem is solved considering this 3 theorems about triangles
exterior angle of a triangle theoremlinear pair theoremsum of angles in a triangleexterior angles theorem: m∠2 + m∠3 = m∠6
If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
Linear pair theorem: m∠5 + m∠6 =180°
Linear pairs are particular instances of supplementary angles that only involve two neighboring angles.
Sum of angles in a triangle is equal to 180 degrees:
m∠2 + m∠3 + m∠5 = 180°
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Solve the inequalityr divided by negative 2.5 is less than or equal to 8.7 for r.
Answer:
r ≤ -21.75
Step-by-step explanation:
Forming the equation,
→ r ÷ (-2.5) ≤ 8.7
Then the value of r will be,
→ r ÷ (-2.5) ≤ 8.7
→ r ≤ 8.7 × (-2.5)
→ r ≤ -21.75
Hence, value of r is -21.75.
Is -1 8/9 a repeating decimal or Terminating
Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?
The total amount of the money earned by Paige will be $1591.92.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.
The total amount of earnings will be,
TA = ( 50 x 30 ) + ( 0.02 x 4596)
TA = 1500 + 91.92
TA = $1591.92
Therefore, the total amount of the money earned by Paige will be $1591.92.
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what is 4x multipied by 7y
Answer:
Step-by-step explanation:
28xy
10. On a school trip the ratio of the number of teachers to the number of students is 1 : 15
The ratio of the number of male students to the number of female students is 7:5
Work out what percentage of all the people on the trip are female students.
Give your answer correct to the nearest whole number.
There are 39% of all the people on the trip are female students on a school trip.
What is meant by the term ratio?Mathematicians use the term "ratio" to compare two numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities being compared using division in a ratio.One to fifteen teachers are assigned to every hundred students.
and there are 7:5 more female students than male students.
Let's say there are x teachers. Students multiply by 15 as a result.
Take the ratio of male to female as 7 years for the male and 5 years for the female.
The total student trip is made up of both male and female pupils.
Thus,
15x = 7y + 5y
15x = 12y
5x = 4y
x = 4/5y ...eq 1
Then, the percentage of the female students.
5y/(x + 5x)×100
5y/16x ×100
Put the value of x from eq 1
625/ 16 = 39%
Thus, there are 39% of all the people on the trip are female students.
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You have eight marbles. all the marbles weigh the same, except for one, which is heavier than all the others. the marbles are otherwise indistinguishable. you may make no assumptions about how much heavier the heavy marble is. the task is to find the heavy marble by using a two-pan balance what is the minimum number of weighings required to identify the heavy marble?
A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.
As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.
Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.
The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.
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A line segment is shown on the coordinate grid.
What is the domain displayed on the line graph above?
Answer: x = -2 through 1
Step-by-step explanation:
The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!
8. The length of a rectangle is 3 feet longer than the width. If the width is x feet, how long is the rectangle?
Answer:
Let the width be x feet. As length is 3 feet longer, it is x+3 feet. As perimeter is twice of te sum of length and width, it is 2×(x+3+x)=2×(2x+3)=4x+6 feet.
Step-by-step explanation:
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=8.4 and x=7.3 and passes through the point (0,8.2).
Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)
What is parabola?The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.
According to given data:We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)
As we parabola is quadratic function,
f(x) = a(x-8.4)(x-7.3)
It is passing through the point (0, 8.2)
8.2 = a(-8.4)(-7.3)
a = 8.2/61.32 =7.5 (approx)
Now, equation of parabola is
F(x) = 7.5(x-8.4)(x-7.3)
f(x) = 7.5(x^2-7.3x-8.4x+61.32)
F(x) = 7.5(x^2-15.7x+61.32)
Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).
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Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
The equation 22+(d-1)0.5 = 30 may be used to determine how many days it will take the plant to reach a height of 30 cm. The value of d is 17, and it stands for the number of days.
What is an arithmetic sequence?There are two definitions for an arithmetic sequence. It is a series where the differences between every two succeeding terms are identical or each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term.
The following details are available to us:
A 22 cm tall basil plant that is gaining half a centimeter daily was purchased by Matteo.
We now have the arithmetic progression shown below with the common difference, indicated by the letter d:
22, 22.5, 23, 23.5, ...
The formula for calculating the nth term:
When an is the first term, a(n) = a+(n-1)d.
A) 22+(d-1)0.5 = 30
B) The plant still needs to develop 8 cm, as there is a difference of 8 cm between 30 and 22.
C) D's value:
22+(d-1)0.5 = 30
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123 1/23 +(−123 1/23 )
Answer: positive
Step-by-step explanation:
123 1/23 + (-123 1/23)
123 1/23 - 123 1/23 = 0
0 is a positive number and not negative so the answer is negative
in a right triangle, the longer leg is two more than three times the shorter leg, and the area of the triangle is 400. what is the length of the shorter leg?
The length of the shorter leg is 16 units which was found using the given data.
What exactly is a quadratic equation?A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.
Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.
We know that,
Area of triangle = 1/2(larger leg)(shorter leg)
400=1/2(larger leg)(shorter leg) Equation(1)
larger leg = 2 + 3(shorter leg)
We need to substitute this in Equation(1)
400 = 1/2[2+3(shorter leg)](shorter leg)
800 = 2(shorter leg) + 3(shorter leg)²
3(shorter leg)² + 2(shorter leg) - 800 = 0
Solving this quadratic equation,
we get, shorter leg = - 16 or +16
Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.
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Calculate S16 for the arithmetic sequence defined by (an) = {5/8-5/16n}
65/
2
65/
8
-65/
8
-65/
2
The sum of the first 16 terms of the defined arithmetic sequence is given as follows:
-520/16.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the equation presented as follows, called general equation:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the arithmetic sequence.
The sum of the first n terms is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The sequence in this problem is defined as follows:
[tex]a_n = \frac{5}{8} - \frac{5}{16}n[/tex]
The first term is of:
[tex]a_1 = \frac{5}{8} - \frac{5}{16} = \frac{5}{16}[/tex]
Hence the 16th term of the sequence is of:
[tex]a_{16} = \frac{5}{8} - \frac{5}{16}(16) = \frac{5}{8} - 5 = -\frac{35}{8}[/tex]
Hence the sum of the first 16 terms of the arithmetic sequence is defined as follows:
[tex]S_{16} = 8\left(\frac{5}{16} - \frac{35}{8}\right) = 8 \times \left(-\frac{65}{16}\right) = -\frac{520}{16}[/tex]
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
250 bicycles must be manufactured to minimize the cost.
The cost C in dollar of manufacturing x bicycles at a production plant is given by:
C(x) = 3x² - 1500x + 198,500
a. To find number of bicycle that can minimize the cost
differentiate C(x) with respect to x
C'(x) = 6x - 1500
equating C'(x) = 0
6x - 1500 = 0
x = 1500/6
x = 250 , is our stationary point
Differentiate C'(x) = 6x - 1500 again and put x = 250,
C''(x) = 6 (positive)
At x = 250 , cost is minimum
Therefore , 250 bicycles must be manufactured to minimize the cost.
b. C(x) = 3x² - 1500x + 198,500
putting x = 250,
C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500
= $11,000 is the minimum cost
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A, B and C are points on the circumference of a circle.
XY is a tangent to the circle at the point A.
Angle BAY = 72° and angle ABC = 54°.
Prove that triangle ABC is an isosceles
triangle.
You must give a reason for any statement
that you make or any calculation that you
carry out.
By using tangent property of circle, it has been proved that [tex]\Delta[/tex] ABC is isosceles
What is tangent to a circle?
At first it is important to know about circle.
Circle is a two dimensional round figure in which every point of the circle maintains a fixed distance from a point known as the center. The fixed distance is called the radius of the circle.
The straight line which touches the circle at any point is known as the tangent to a circle.
Tangent property of circle is used here
[tex]\angle BAY = 72^{\circ}[/tex]
[tex]\angle ABC = 54^{\circ}[/tex]
[tex]\angle ACB = 72^{\circ}[/tex] [Angle in alternate segment are equal]
[tex]\angle BAC = 180 - (54 + 72)\\[/tex] [Sum of three angles of a triangle is 180°
= 180 - 126
= 54°
[tex]\Delta ABC[/tex] is isosceles
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Can someone help me on this
The algebra properties associated to each case are listed below:
Case 1: Distributive property
Case 3: Associative property (multiplication)
Case 5: Existence of inverse (addition)
What algebra properties are used in algebraic expressions?
In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:
Reflexive property of equalities.Symmetric property of equalities.Transitive property of equalities.Compatibility property (addition, multiplication)Commutative property (addition, multiplication).Associative property (addition, multiplication).Existence of inverse (addition, multiplication).Modulative property (addition, multiplication).Distributive property.Now we proceed to determine the property associated to corresponding operation:
Case 1
9 · (x + y) = 9 · x + 9 · y → Distributive property
Case 3
[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)
Case 5
(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)
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Andrew owns stock in Hyren Airlines and as a result gets paid dividends worth $539.70 every year. If Andrew owns 105 shares of Hyren Airlines, how big is the dividend each share yields?
Answer: $5.14
Step-by-step explanation:
divide $539.70 by 105 to get the answer
so 539.70 divide by 105 is 5.14
step1 get rid of the decimal but you will ad it later so
53970
/ 105
=514
step2 move the decimal 2 places to the left.
Wyatt is saving money for a PS5 but has to pay back
the $3 he owes his sister.
#5.
Drag the green points so that the shaded region covers
the range.
#6.
What is the range of this function? (Consider: How do
you think the arrow affects the range?)
Answer:
Step-by-step explanation:
dees
A utility pole has a support wire that reaches from the top of the pole to the ground, forming a right triangle. Ryan has measured the angle of elevation to the top of the pole formed by the wire and the ground to be 59°. He also knows that the horizontal distance from the base of the pole to the wire is 7 meters. What is the approximate height of the utility pole? A. 8 meters B. 12 meters C. 11 meters D. 14 meters
The height of utility poles is B. 12 meters.
The height of the utility pole will be calculated by the formula -
tan theta = perpendicular ÷ base, where theta is the angle of elevation, perpendicular is the height of utility pole and base is the distance from the base of pole to the wire.
Keep the values in formula to find the height of utility pole.
tan 59 = perpendicular ÷ 7
Perpendicular = tan 59 × 7
Perpendicular = 1.66 × 7
Performing multiplication on Right Hand Side of the equation
Perpendicular = 11.65 metres
On rounding off, we get 12 metres.
Thus, the height is B. 12 meters.
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A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 175 m downhill from the base of the tower. The angle in the figure is determined to be 13°. Find the length of cable required for the guy wire. (Round your answer to the nearest meter.)
Answer:
ii think that the figure will be determined by 13#
Step-by-step explanation:
you have to round up to the nearest meter
PLEASE HELP MEE!
Solve x2 – 2x = 15 by applying the quadratic formula.
HELP MEEE PLEASEEEEE
Answer:
XY = 12.4 cm
Step-by-step explanation:
a² + b² = c²
(4 cm)² + (XY)² = (13 cm)²
16 cm² + XY² = 169 cm²
XY² = 153 cm²
XY = √(153 cm²)
XY = 12.4 cm
if three sides of a trapezoid are 10 inches long, how long should the fourth side be if the area is a maximum?
The area of the trapezoid is maximum when the fourth side be 20 inches.
What is meant by trapezium?Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.
By applying Pythagorean theorem,
[tex]c^2=a^2+b^2[/tex]
[tex]10^2=h^2+x^2[/tex]
[tex]100=h^2+x^2[/tex]
[tex]h^2=100-x^2[/tex]
[tex]h=\sqrt{100-x^2}[/tex]
Area of the trapezoid is,
[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]
By substituting the values of h, b1, and b2 in the above equation,
[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]
[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]
If we take the derivative of both sides of the equation in relation to x, we get
[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]
[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\frac {dA}{dx}=0[/tex]
[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]
100-x²=x²+10x
2x²+10x-100=0
x²+5x-50=0
(x-5)(x+10)=0
If, x+10=0
x=-10
The above value is not accepted because it is a negative value,
If, x-5=0
x= 5
The value is accepted because it is positive value
The length of the trapezium which should be fourth is,
b₂=2x+10
b₂= 2(5)+10
b₂=20
The area of the trapezoid is maximum when the fourth side be 20 inches
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A 2-pint carton of non-dairy creamer costs $3.36. What is the price per cup?
Answer:
$6.72
Step-by-step explanation:
1 us liquid pint =2 us cups
3.36*2 cups
4/9 - 1/2 Subtract.
- Simplest form.
-1/9 - (-2/5) Evaluate.
- Simplest form.
Answer:
Step-by-step explanation:
Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18
The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.
help meeeeeeeeeeeeeeeeee please
Answer:
324 ft
Step-by-step explanation:
[tex]v=\sqrt{2gh}[/tex]
[tex]v^2=(\sqrt{2gh})^2[/tex]
[tex]v^2=2gh[/tex]
[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]
[tex]\frac{v^2}{2g}=h[/tex]
[tex]\frac{144^2}{2(32)}=h[/tex]
[tex]\frac{20736}{64}=h[/tex]
[tex]324=h[/tex]
Consider the system of equations : 2a + 3b - 4c = 7,
a - b + 2c = 6
(a) Find an ordered tripe of numbers (a,b,c) that satisfies both equations.
(b) Can you find a second ordered triple that satisfies both equations.
(c) Solve for b in terms of a, and solve for c in terms of a. How many solutions does this system have?
Answer:
a. 87 b. 9 c. 4
Step-by-step explanation:
cual es el interes que genera $600, colocados al 8% anual durante 1 año 4 meses?
The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64
Simple InterestThe formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.
Simple interest formula is given as:
S.I = P(1 + rt)
S.I = Simple InterestP = principalr = rate t = timeSubstituting the values into the formula
S.I = 600(1 + 0.08 * 16)
S.I = 664
The interest generated is $64
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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?
a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?
An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
Given that;
The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,
Let 'T' be the number of times the price is decreased.
So, price;
p = 38 – 5x
x = (38 - p) / 5
And as per the given condition attendance;
a = 1000 + 50x
So, the Revenue is;
To develop an equation for revenue (r) as a function of p, the price of tickets;
R = p * a
R= p * (1000 + 50x)
But, x = (38 - p) / 5
Then,
R = P * (1000 + 50(38 - p)/5)
= p * (1000 + 380 - 10p)
= p * (1380 – 10p)
= 1380p - 10p² → (I)
To get R(25) from (I);
R(25) = 1380(25) - 10(25)²
= 34500 - 6250
= 28250
Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
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A person invests 4500 dollars in a bank. the bank pays 7% interest compounded annually. to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14900 dollars?
Answer:
A = Ao * (1+ i)^n amount Ao invested for n yrs at i/yr
14900 = 4500 (1.07)^n
3.311 = (1.07)^n
log 3.311 = n log 1.07 = n* .0294
n = log 3.311 / .0294 = .52 / .0294 = 17.6 yrs
Check:
Money will double about very 70 / 7 = 10 yrs
At 10 yrs around 9000 return
At 20 yrs 18,000 return - result appears reasonable