The coordinates of the 4th vertex of the rhombus are (-2,3)
How to determine the coordinates of the 4th vertex?The diagonals are given as:
(-7, -2) and (-1, -4)
The 3rd vertex is given as: (-6,-9)
Calculate the distance between the vertices of the diagonals and the 3rd vertex using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50[/tex]
[tex]d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50[/tex]
Let the 4th vertex be (x,y)
So, we have:
[tex]d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50[/tex]
[tex]d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50[/tex]
Equate d3 and d4
[tex]\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}[/tex]
Take the square of both sides
[tex](-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2[/tex]
Expand
[tex]1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2[/tex]
Evaluate the like terms
1 + 2x + 16 + 8y = 49 + 14x + 4 + 4y
Collect like terms
14x - 2x + 4y - 8y = 1 + 16 - 49 - 4
12x - 4y = -36
Divide through by 4
3x - y = -9
Next, we test the options in the above equation
Point (-8,13) means x = -8 and y = 13
So, we have:
3x - y = -9
3(-8) - 13 = -9
-37 = -9 --- this is false
Point (-2, 3) means x = -2 and y = 3
So, we have:
3x - y = -9
3(-2) - 3 = -9
-9 = -9 --- this is true.
Hence, the coordinates of the 4th vertex are (-2,3)
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Saul correctly solved a math problem by first dividing 18 by 6, then adding 5 to the result.
Which equation could be solved to get the same answer?
6x−5= 18
6(x−5)=18
6x+5=18
6(x+5)=18
Answers.
[tex] \frac{23}{6} [/tex]x=8[tex] \frac{13}{6} [/tex]x=-2
I need help with 7 and 4 and 9 also 10
I will give the most higher points I got
a house and lot cost $120,000. if the house cost 3 times more than the lot, how much did the house cost?
Answer:
$90,000
Step-by-step explanation:
We can can use substitution for this. First, we need to create two separate problems that represent this situation. The house and the lot together cost 120000, so we can make the equation h+l=120000. We also know that the house is worth 3 lots, so we can make the equation h=3l. Because h=3l, we can substitute for h, making the equation 3l+l=120000, or 4l=120000. To isolate l, we have to divide both sides by 4. If we do that, we get l=30000. Now, we have to substitute to find h. Our new equation is h+30000=120000. To isolate h, we have to subtract 30000 from each side. If we do this, we get h=90000. That's our answer.
Hope this helps!
What is the next number in this sequence?
38 57 76
Answer:
the next sequence is 76+19= 95
Answer:
Next number = 95
Step-by-step explanation:
Hi! Let me help you out.
_________________
To determine the next number in this sequence, we should determine the common difference.
We can do it like this.
[tex]\longmapsto\sf 76-57=19[/tex]
See. I took the third term, and subtracted the second term from it.
Continue.
[tex]\longmapsto\sf 57-38=19[/tex]
↪
The number we obtain after subtracting is the common difference.
So we should take the third term, "76", and add the common difference, "19" to it.
We obtain 95. Which is the final answer.
⇨Hope that this helped you out! have a great day ahead.⇦
Best Wishes!
[tex]\star\bigstar\overline{\textsf{Reach far. Aim high. Dream big.}}[/tex]
◆◈-Greetings!-◈◆
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One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the length of the hypotenuse.
In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearesttenth of a cm, how long is that leg?
Evaluate: sin (Arccos(5/13))
Evaluate: tan(Arctan(π/6))
1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,
[tex]x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}[/tex]
This means that the length of the hypotenuse is:
[tex]\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}[/tex]
2) (Diagram attached) We know that
[tex]\cos 51^{\circ}=\frac{x}{58}\\x=58 \cos 51^{\circ} \approx \boxed{36.5}[/tex] (in cm)
3) From the Pythagorean identity,
[tex]\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}[/tex]
4) [tex]\frac{\pi}{6}[/tex]
Bailey went out to dinner. It cost $ 45.00. He wanted to leave a 20% tip for his waitress. Find the tip.
Answer:
The tip should be $9.00
Step-by-step explanation:
If you can please give me a step by step explanation
Step-by-step explanation:
4(y+8)=9
for this sum first we need to multiply 4to y and 4 to 8
4y+32=9
then u need to -9 from both sides
4y=23
y=23/4
u will get the answer
Solve the following inequality using both the graphical and algebraic approach: 8 minus x greater-than-or-equal-to 5 (8 minus x) Graph A On a coordinate plane, a line goes through (0, 8) and (8, 0). Another line goes through (8, 0) and (7, 10). Graph B On a coordinate plane, a horizontal line is at y = 5 and another line goes through (8, 0) and (0, negative 8). a. x greater-than-or-equal-to 8 Graph A b. x less-than-or-equal-to 8 Graph A c. x greater-than-or-equal-to 8 Graph B d. x less-than-or-equal-to 8 Graph B
The given inequality (8 - X ≥ 5(8 - x)) is solved using graphs method and the result is (Option A); that is x ≥ 8 Graph A.
The inequality is given as: 8-x≥5(8-x)
The next step algebraically is to open the brackets. Hence,
8-x ≥ 40 -5x
Next, we collect like terms
= -x+5x ≥ 40-8
= 4x ≥ 32
Make x the subject of the statement by dividing both sides with 4
= x ≥ 8
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M
x-2
20
L
Find the value of x.
A.2
B.4
C.6
D.8
Answer:
X=4
Step-by-step explanation:
Eveything is explained in the pic. Hope that helps ;)
Argelis had þhe following containers of paint leftover, 1/2 gallon, 3/4 quarts and 1/4 gallon. How many quarts of paint does argelis have left
3.75 quarts of paint does Argelis have left with her.
What is Gallons?A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces.
Here, we know that,
1 gallons = 4 quarts
so, 1/2 gallons = 1/2 X 4 = 2 quarts.
and 1/4 gallons = 1/4 X 4 = 1 quarts.
Now, total paint left with Argelis = 1/2 gallons + 3/4 quarts + 1/4 gallons
= 2 quarts + 3/4 quarts + 1 quarts
= 3 quarts + 3/4 quarts
= 15/4 quarts or 3.75 quarts
Thus, 3.75 quarts of paint does Argelis have left with her.
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How does the graph of y = a(x – h)^2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. The vertex of the graph moves to a point half as far from the x-axis. The vertex of the graph moves to a point half as far from the y-axis.
The vertex of the graph moves to a point twice as far from the y-axis.
Option B is the right answer.
What is the equation of Parabola ?The general equation of a parabola is
y = a(x-h)² + k
or
x = a(y-k)² +h
where (h,k) denotes the vertex.
It is given in the question that the value of h is doubled for the equation given
y = a(x-h)² + k
if the value of the h is doubled, the vertex of the graph shifts and shifts on the x axis away from the y axis , therefore
the vertex of the graph moves to a point twice as far from the y-axis.
Option B is the right answer.
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Answer:
its b
Step-by-step explanation:
What is the probability of picking a blue marble and flipping heads?
Answer:
7/11
Step-by-step explanation:
blue = 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7 that will be blue.
green = 1 + 1 + 1 + 1 = 4 that will be green.
So it’s going to be 7 + 4 = 11 in total then do
7/11
Is it 7/22
what is the transformation
(x,y) (x+5,y -3)
(x -5, y+3)
(x+3 y-5 )
x-3,y +5
what is the symbol called ? (i just need the symbol dont solve!)
Answer:
The symbol is a variable called x, which is a mathematical term used to substitute values in mostly linear and quadratic equations.
Answer:
a term.
Step-by-step explanation:
(I'm assuming you're asking about the underlined,)
therefore the 9x is a term
(top line)
the 9 is a coefficient
the x is a variable
5 is a constant
- (subtraction sign) is the operator.
9x - 5 is an expression
(bottom line)
the 3x is also a term
x is the variable
3 is a coefficient
4 is the constant
the + (addition sign) is the operator
3x + 4 is the expression.
the answer would be a constant and a term
hope this helps:)
Lawrence needs to be at his job by 5:00 p.m.
It takes him 20 minutes to ride his bike to his job, 30 minutes to eat dinner, and 45 minutes to do his homework.
Which time does he need to start his homework?
A.
3:00 p.m.
B.
3:25 p.m.
C.
3:35 p.m.
D.
4:20 p.m.
Answer:
B. 3.25 p.m.
Step-by-step explanation:
[tex]20 + 30 + 45 = 96 \: minutes \\ 95 \: minutes \: = 60 \: minutes + 35 \: minutes \\ 95 \: minutes \: = 1 \: hour \: 35 \: minutes\\ 5.00 \: p.m. - 1 \: hour \: 35 \: minutes = 3.25 \: p.m.[/tex]
d=√(-4-42.78)^2 + (3-44.78)^2
The expression is equal to 3sqrt(517)/5
Learners have to demonstrate knowledge and skills in calculating quantities
such as mass, length, perimeter, temperature and the volume of objects. When
teaching conversions, emphasis must be placed on multiplication by a
thousand (since "kilo" means thousand) and one thousandth (since "milli"
means one thousandth). Design an instructional activity to explain how you
would teach grade 4 learners the conversion of units when measuring length.
Refer to page 25 of the CAPS document, the second bullet under
‘Calculations and problem-solving involving length’. Your focus should be
on whole number
The instructional activity to explain the conversion will be:
What real-life situations require you to convert measurements from one unit to another?What is the difference between standard and metric measurement? What should the conversion lessons include?The lessons should include:
How to convert within standard units of distance, mass, and timeThe relationship between metric conversions and decimal numbers in the base-ten systemHow to convert metric measurements of distance and mass.Learn more about instructional activity on:
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The length of ribbon A is 56 feet and the length of ribbon B is 59 feet.
The exact length of ribbon C is 34 feet longer than the estimated difference in lengths of ribbon A and B.
What is the length of ribbon C?
Note - Use 0,12 or 1 as benchmarks.
The length of ribbon C is 37 feet.
What is the length of ribbon C?The equation that can be used to determine the length of ribbon C is:
C = 34 + ( length of ribbon B - length of ribbon A)
C = 34 + (59 - 56)
C = 34 + 3
c = 37 feet
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write an even number between 7 and 16 draw a picture and then write a sentence to explain why it is an odd number
Answer: An even number between 7 and 16 would be 10.
Step-by-step explanation: I am not sure how I am supposed to draw a picture of the number other than drawing the number itself. However, 10 is an even number because it is a composite number and is divisible by 2. 10 is an even number, not an odd number. Hope this helps!
what is the vertex of y= -x^2+10x
[tex]y = -x^2+10x\implies y = -x^2+10x+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 10}{2(-1)}~~~~ ,~~~~ 0-\cfrac{ (10)^2}{4(-1)}\right)\implies \left( \cfrac{10}{2}~~,~~\cfrac{100}{4} \right)\implies (5~~,~~25)[/tex]
what's a quarter of 46.5
Answer:
11.625 or mixed number form 11 [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
divide 46.5 by 4
Y=-2x²-4 solve for y when x=3
Answer:
Y=-58
Step-by-step explanation:
Y=-2(3)^(2)-4
Y=-2(3*3*3)-4
Y=-2(27)-4
Y=-54-4
Y=-58
( PLEASE HELP WITH THIS QUESTION)
You are studying a single-celled organism under a microscope. Is it possible for this organism to be classified as fungi?
Answer: Yes it is possible
Example: Yeast is a single-celled fungus.
There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.
Use SOHCAHTOA to find the side measure. Show work. Round to one decimal place.
The value of the n is 64.04 after applying the tan ratio which is opposite to adjacent (TOA)
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a right angle triangle shown in the picture.
We can use SOHCAHTOA to find the unknown length.
Using the ratio of tan which is opposite to adjacent (TOA)
tan8 = 9/n
n = 64.038 ≈ 64.04
Thus, the value of the n is 64.04 after applying the tan ratio which is opposite to adjacent (TOA)
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17.
select the correct answer
what is the equation of the problem shown with its focus on this graph?
Options are in photo!
Answer:
B
Step-by-step explanation:
Pls help me with number
Answer:
Total people = 240
Step-by-step explanation:
Let the total number of people by 'x'.
[tex]\sf \text{Number of men =$ \dfrac{1}{4}*x$} \\[/tex]
[tex]\sf \text{Number of women =$\dfrac{1}{3}x$}[/tex]
Number of children = 100
When we subtract the total number of men and women from the total people 'x', we get the number of children.
[tex]\sf x - \left(\dfrac{1}{4}x+\dfrac{1}{3}x\right)= 100\\\\x - \left(\dfrac{1*3}{4*3}x+\dfrac{1*4}{3*4}x\right)=100\\\\[/tex]
[tex]x- \dfrac{4+3}{12}x=100\\\\x - \dfrac{7}{12}x = 100\\\\ \dfrac{12}{12}x-\dfrac{7}{12}x = 100\\\\ \dfrac{5}{12}x=100\\[/tex]
[tex]\sf x = 100*\dfrac{12}{5}\\[/tex]
x = 20 * 12
x = 240
Total number of people = 240Please help , I litteraly have a F in Math
Answer:
A=3
B=31
Step-by-step explanation:
A)5-2=3
b)
17-10=7
10-5=5
7-5=2
2×7=14
14+17=31
which expression is equivalent to (3x² + 3x - 3) - (6x² - 4x - 2)?
Answer:
A. [tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]
Step-by-step explanation:
For this problem, we have to combine like terms.
Let's look at the equation:
[tex](12x^{4} -4x^{3} +7x+6)+(3x^{2} -4x+14)[/tex]
[tex]12x^{4[/tex], [tex]-4x^{3}[/tex], [tex]3x^{2}[/tex] do not have any other like terms, so we keep all in the final answer.
[tex]7x[/tex] and [tex]-4x[/tex] are like terms, so we combine them. [tex]7x-4x=3x[/tex]
14 and 6 are like terms, so we combine them. 14+6 = 20
Let's put everything into the final equation:
[tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]
So, the final answer is A. [tex]12x^{4} -4x^{3} +3x^{2} +3x+20[/tex]
Hope this helps! If you have any questions about my work, leave them in the comments below!
if a quarter kilogram costs rs 60 then how much will cost for 150 grams
Answer:
R s. 36
Step-by-step explanation:
1kg ⇒ 1000g
So, a quarter kilogram means,
[tex]\frac{1}{4}[/tex] × 1kg = 1000g × [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{4}[/tex] × 1kg = 250g
According to the question,
250g = R s. 60
So, now they're asking for the price of 150g.
Let that price be x.
250g ⇒ R s. 60
150g ⇒ x
Use cross multiplication to find the value of x.
250x = 60 × 150
250x = 9000
Divide both sides by 250.
x = R s. 36
Translate this phrase into an algebraic expression.
8 more than twice Jenny's age
Use the variable j to represent Jenny's age. Please help.. :(
Answer:
2j + 8
Step-by-step explanation:
Given: 8 more than twice Jenny's age
Let j = Jenny's age
"twice Jenny's age" means double (multiply by 2) Jenny's age = 2j
"more than" means to add, so "8 more than" = + 8
Therefore:
"8 more than twice Jenny's age" = 2j + 8