Answer: One triangle
Step-by-step explanation:
-The triangle's dimensions are defined and fixed.
-Given the fixed dimensions, only one unique triangle can be constructed.
-Hence, only one triangle of the dimensions 7.2cm, 6.9cm and 12.8 cm can be formed.
Answer:
1
Step-by-step explanation:
The correct shape would be a scalene triangle, which can't be bent and twisted and still have the same side lengths.
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Three vertices of parallelogram PQRS are show: Q(8, 5), R(5, 1), S(2, 5)
Place statements and reasons in the table to complete the proof that shows that parallelogram PQRS is a rhombus.
[tex]PQRS[/tex] is a rhombus since [tex]\overline{QR} \cong \overline{RS}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex], [tex]m\angle R \neq 90^{\circ}[/tex] and [tex]m\angle R \neq 180^{\circ}[/tex]. [tex]\blacksquare[/tex]
How to demonstrate that a given figure represents a rhombus
In this question we must prove that a given parallelogram is a rhombus. A rhombus is quadrilateral with four sides of equal length and two pairs of angles of equal measure, different to each other. We must demonstrate that [tex]\overline {QR} \cong \overline {RS}[/tex] and [tex]m\angle R \neq 90^{\circ}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex] and [tex]m\angle R \neq 180^{\circ}[/tex] by geometric and algebraic definitions and theorems:
[tex]Q(x,y) = (8,5)[/tex], [tex]R(x,y) = (5,1)[/tex], [tex]S(x,y) = (2,5)[/tex] Given[tex]QR = \sqrt{(5-8)^{2}+(1-5)^{2}} = 5[/tex] Pythagorean theorem/Line segment length formula[tex]RS = \sqrt{(2-5)^{2}+(5-1)^{2}} = 5[/tex] Pythagorean theorem/Line segment length formula[tex]QR = RS[/tex] (2) and (3)[tex]\overrightarrow {QR} \,\bullet\,\overrightarrow{RS} = (-3)\cdot (-3) + (-4)\cdot (4) = -7[/tex] Dot product[tex]\theta = \cos^{-1}\left(\frac{\overrightarrow{QR}\,\bullet\,\overrightarrow{RS}}{QR\cdot RS} \right) = \cos^{-1}\left(-\frac{7}{25} \right) \approx 106.260^{\circ}[/tex] Dot product[tex]\overline{QR} \cong \overline {RS}[/tex] (4) and (6)[tex]PQRS[/tex] is a rhombus. (6) and (7)/Result[tex]PQRS[/tex] is a rhombus since [tex]\overline{QR} \cong \overline{RS}[/tex] and [tex]m\angle R \neq 0^{\circ}[/tex], [tex]m\angle R \neq 90^{\circ}[/tex] and [tex]m\angle R \neq 180^{\circ}[/tex]. [tex]\blacksquare[/tex]
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Nina’s sister has 386 stickers that she wants to put in a book. Each page can hold 42 stickers. How many pages will she need? Explain your reasoning.
Answer:
10 pages
Step-by-step explanation:
386/42=9.1 pages
but you can not have .1 of a page so you add another page.
Two joggers set out at the same time from their homes 21 miles apart. They agree to meet at a point somewhere in
between in an hour and a half. If the rate of one is 2 mph faster than the rate of the other, find the rate of each
The two joggers who are 21 miles apart travel at a speed 8 mph and 6 mph respectively and would meet after one and half hours.
What is an equation?An equation is an expression used to show the relationship between two or more variables and numbers.
Let a represent the speed of the faster jogger and represent the speed of the other jogger. Hence:
a = b + 2 (1)
Also:
In one and half hour (1.5 h):
a = d₁/1.5
d₁ = 1.5a
b = d₂/1.5
d₂ = 1.5b
d₁+ d₂ = 21
1.5a + 1.5b = 21 (2)
From both equation 1 and 2:
a = 8, b = 6
The speed of the joggers is 8 mph and 6 mph respectively.
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What is the value of the expression 3x-8y when x=10 and y=2?
Answer:
14
Step-by-step explanation:
3x-8y
(3*10)-(8*2)
30-16
14
Answer:
30-16
Step-by-step explanation:
does anybody know how
what is the line of symmetry of the parabola y=x2+6×-9
x=6
x=-9
×=-3
Answer:
x = - 3
Step-by-step explanation:
given a parabola in standard form y = ax² + bx + c (a ≠ 0 )
then the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 6x - 9 ← is in standard form
with a = 1, b = 6 , then the equation of the axis of symmetry is
x = - [tex]\frac{6}{2}[/tex] = - 3 , that is x = - 3
The original price of a T-Shirt is $15. The T-Shirt is on sale for 35% off. What is the sale price?
Answer:
9.75$
Step-by-step explanation:
Answer:
9.75$
Step-by-step explanation:
The original price of the shirt is $15, and it's on sale for 35% off. What is the item's sale price?
First, convert the 35% to a real mathematical number. For percents, this is always done by dividing the 35% by 100%, or 35% / 100% = 0.350.
Second, find out what 35% of $15 is. This is the amount of the sale discount. This is always found by multiplying 0.350 by the item's cost $15, like this:
0.350 x $15 = $ 5.25.
So for this sale, you'll save $ 5.25 on this item.
This means, the cost of the item to you is
$15 - $ 5.25 = $ 9.75.
Using the fundamental theorem of algebra how many solutions will the function have, f (x) = 82x^3+ 216
Answer:
The number of solutions is equal to the highest power exponent.
That is a cubic equation, so it has 3 solutions.
Step-by-step explanation:
If a student has a 60 percent in math what will he need to pass semester 2
Answer:
Step-by-step explanation:
Letter Grade Percentage Points Level
A+ 95-100 4.00 Exceptional
A 90 to less than 95 3.75 Excellent
B+ 85 to less than 90 3.50 Superior
B 80 to less than 85 3.00 Very Good
C+ 75 to less than 80 2.50 Above Average
C 70 to less than 75 2.00 Good
D+ 65 to less than 70 1.50 High-Pass
D 60 to less than 65 1.00 Pass
F Less than 60 0.00 Fail
Help me pleaseeee the weekends almost over and it’s due like tomorrow :(
PLEASE help me with #2 i’m struggling DUE TODAY
Solve for x. 3x²+13x=10 Enter your answers in the boxes.
Answer:
2/3 or -5 is correct for all future users.
Step-by-step explanation:
The roots of the quadratic equations or the values of x are -5 and 2/3.
What is a quadratic equation?A quadratic equation is an algebraic equation of degree two. An algebraic equation of degree n has exactly n number of roots.
Given a quadratic equation 3x² + 13x = 10 which can be written as,
3x² + 13x - 10 = 0.
Now two numbers that add to 13 and multiplied to -30 are 15 and - 2.
3x² + 15x - 2x - 10 = 0.
3x(x + 5) - 2(x + 5) = 0.
(x+5)(3x-2) = 0.
x + 5 = 0 OR 3x -2 = 0.
x = -5 OR x = 2/3.
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The leading brand of lipstick in the US had about 20% of the total sales in the industry. The total sales were $200,000 What was the leading brands sales? Show your work
Answer:
200*20
÷100 ,=100+56
29+63
Step-by-step explanation:
200×20 =40000
40000÷100 =
100
a water bottle has a capacity of 25oz.. How many cups of water will the water bottle hold.
Answer:
3.125 U.S. cups
take how many cups are in one ounce and multiply it.
What civilization found the first known value of pi?.
Answer: The Egyptians, Babylonians, and Archimedes.
Step-by-step explanation: The Egyptians and Babylonians were the first known civilizations to use pi. At the time, Egyptians devised the approximated value of pi as 3.1605. Archimedes, however, did the first calculation of pi, with its approximate value of 3.141592 or 3.14 to make it shorter.
Hopefully, this helps you!
Pls help I'll give brainly i really need it
hello
30/42 = x /49
42 x = 1 470
x = 35
30 /42 = 40/ 40 + y
30 y + 1200 = 1 680
30 y = 1 680 - 1 200
30 y = 480
y = 16
Answer:
x = 35
y = 16
Step-by-step explanation:
Both the triangles are similar by AA test of similarity.
[tex] \implies \: \frac{30}{30 + 12} = \frac{40}{40 + y} = \frac{x}{49} \\ \\ \implies \: \frac{30}{42} = \frac{40}{40 + y} = \frac{x}{49} \\ \\ \implies \: \frac{5}{7} = \frac{40}{40 + y} = \frac{x}{49} \\ \\ \implies \: \frac{5}{7} = \frac{x}{49} \\ \\ \implies \: x = \frac{5 \times 49}{7} \\ \\ \implies \huge \red {\boxed{ \: x = 35}}\\ \\ \implies \: \frac{5}{7} = \frac{40}{40 + y} \\ \\ 5(40 + y) = 280 \\ \\ \implies \: 200 + 5y = 280 \\ \\ \implies \: 5y = 280 - 200 \\ \\ \implies \: 5y = 80 \\ \\ \implies \: y = \frac{80}{5} \\ \\ \implies \: \huge { \orange{ \boxed{ y = 16}}}[/tex]
8) At a recent party, it cost $18.50 for refreshments for 10 guests. At this rate, how much would it cost to have refreshments for 80 guests?
Answer:
$148 pretty sure
Step-by-step explanation:
Answer:
$148
Step-by-step explanation:
Divide 18.50 by 10 to get the cost for 1 guest
18.50 / 10 = 1.85
Multiply 1.85 by 80
The admission fee to the Michigan State Fair is $6 for children and $4 for adults. On the first day $1250 was collected. A total of 220 children and adults attended the fair the first day. How many children and how many adults attended the fair the first day?
Write and solve a system of equations to answer the question.
Show your work here:
Question 2
Answer:
children and
adults attended the fair the first day.
Answer:
185 children and 35 adults
Step-by-step explanation:
first equation: 6x+4y=1250
second equation: x+y=220
work:
6x+4y=1250 (-1)
x+y=220 (6) we eliminate x, that's why I multiply each term by 6 and -1
-6x-4y=-1250
6x+6y=1320
2y=70
2y/2=70/2
y=35 (I used y for adults)
x+35=220
x=220-35
x=185 (and I used x for children)
hope this helps you^^
Type the correct answer in the box.
What trigonometric expression can be used to find the value of X? Replace a and b with the correct values
Answer:
a=12 b=25 degrees
Step-by-step explanation:
the tangent of the 25 degree angle gets you your answer
Trigonometry ('triangle', or 'measure') is the branch of mathematics that studies relationships between side lengths or the angles of the triangles
by the question, we have the following parameters:
Vertical Leg = x
Base length = 12
Angle at the vertical side = 25 degrees
The measure of the x is then calculated using the following tangent ratio
tan(x) = Base length / Vertical leg
Substitute known values
tan(x) = 12/x
So, the trigonometric expression that it is be used for find the value of x is tan(x) = 12/x
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2. A businessman starts
with $10 million and
loses $5 million an
hour. How much
money does he have
after eight hours
Answer:
0
Step-by-step explanation:
He loses it all in 2 hours
Answer:
-25 million
Step-by-step explanation:
Because after 2 hours you will lose all of your money and continue to go down into the negatives.
The day after Thanksgiving dinner, Thomas begins a workout that burns 245 calories each day. It took him 2 weeks to burn off the calories he consumed on Thanksgiving. How many calories did Thomas consume on Thanksgiving?
Answer:
3,430 Cal.
Step-by-step explanation:
You would multiply the number of days in a week: 7 by 2 (14) and then multiply that bye 245 = 3,430
Answer:
3,430
Step-by-step explanation:
First we have 2 weeks, there are 7 days in a week.
2 x 7 = 14
He burns off 245 a day. We multiply 245 by 14 to get:
3,430
Write g(x) = 40x 4x2 in vertex form. Write the function in standard form. Factor a out of the first two terms. Form a perfect square trinomial. Write the trinomial as a binomial squared. G(x) = 4x2 40x g(x) = 4(x2 10x) (ten-halves) squared = 25 g(x) = 4(x2 10x 25) – 4(25) g(x) = (x )2 –.
The specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
What is a perfect square polynomial?If a polynomial p(x) can be written as:
[tex]p(x) = [f(x)]^2[/tex]
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial
For the considered case, the polynomial specified is;
[tex]g(x) = 40x + 4x^2[/tex]
Case 1: Converting to vertex form[tex]g(x) = 40x + 4x^2\\g(x) = 4(x^2 + 10) = 4(x^2 + 10 + 25 -25)\\g(x) = 4(x^2 + 10 + 25) - 100 = 4(x+5)^2 - 100\\[/tex]
Thus, the vertex form of the considered polynomial is [tex]g(x) = 4(x+5)^2 - 100[/tex]
Case 2: Converting to standard formStandard form of a quadratic polynomial is [tex]ax^2 + bx + c[/tex]
Thus, we get: the considered polynomial in standard form as:
[tex]g(x) = 4x^2 +40x[/tex]
Case 3: Factoring the first two terms of polynomial[tex]g(x) = 40x + 4x^2 \\g(x) = 4x(10 + x)[/tex]
Case 4: Forming a perfect square trinomialThe considered polynomial has only two terms, therefore, its not a trinomial.
Thus, the specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]
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Answer:
g(x)=4(x+5)^2-100
Step-by-step explanation:
Have the day you deserve :)
Tasha earns $75,000 per year. Her payroll deductions are 28% of her gross income. She saves 5% of her net
income each month in case of an emergency. How much will she budget for her emergency savings for the month
of March?
O $3,750
$312.50
O $87.50
O $225.00
Answer:
87.50
Step-by-step explanation:
75,000 x 28% ÷ 12
She will budget $225 for her emergency savings for the month of March
How to determine the amount saved for emergency?We have:
Gross = $75,000 per year.
Payroll deductions = 28%
So, the net pay is:
Net = (1 - 28%) * $75,000
Evaluate
Net = $54000
The net income per month is:
Monthly = $54000/12
Evaluate
Monthly = $4500
5% of her net income goes to emergency.
So, we have:
Emergency = 5% * $4500
Evaluate
Emergency = $225
Hence, she will budget $225 for her emergency savings for the month of March
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Create a data set that contains 10 values such that the mean is greater than the median.
Answer:
Go with anything, and I mean ANYTHING that is in a numerical order with an outlier
LITERALLY 1,2,3,4,5,6,7,8,9,100
you will get a median of 5.5 but with the high outlier, you will get a mean of 14.5
Max wants to rent a bicycle. The cost to rent a bike is a $5 insurance fee plus $3 per hour. Max has at most $20 to spend. Write an inequality to represent this scenario. Give a value that satisfies the inequality.
Answer: 5 + 3x ≤ 20; 5
Step-by-step explanation:
at most means not more than(less or equal to),which use the symbol ≤. Let x be the hour that Max rent.
5 + 3x ≤ 20
3x ≤ 15 [Subtract 5 from both sides.]
x ≤ 5 [Divide 3 from both sides.]
Any value less than or equal to 5 will be satisfies the inequality.
Give two(2)example of the system of linear inequalities in two variables.
Answer: A linear system of two equations with two variables is any system that can be written in the form. ... A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time. For the example above x=2 and y=−1 is a solution to the system
Step-by-step explanation:
Round each decimal number to the nearest tenth. Then, select the best estimate for the subtraction equation 4.35 − 1.27 = ___.
Answer:
3.1
Step-by-step explanation:
When you round to the nearest tenth 4.35 is 4.4 and 1.27 is 1.3
Answer: 3.1
Step-by-step explanation: Round 4.35 and you get 4.4 round 1.27 you get 1.3 subtract them and you get 3.1
Help with substitution please.
What is the slope of the line shown?
Answers
A: 3
B:2
C:1/2
D:-3