10. rhombus abcd has vertices at a(-2, 7), b(8, 7), c(2, -1), and d (-8, -1).
determine the area of abcd.
Answer: 80
Step-by-step explanation:
We can use the formula [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals.
By the distance formula,
[tex]AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}[/tex]
So, the area is [tex]\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}[/tex]
In the given figure, if y = 30, find (i) x (ii) z and (iii) u
Answer:
u=30
x=150
z=150
y=30
Step-by-step explanation:
u=y [ being vertically opposite angle]
x+u=180[ being linear pair]
x+30=180
x=180-30
x=150
z=x[being vertically opposite angle]
z=150
y=u[ being voa]
Answer:
=40°
Step-by-step explanation:
Sorry that's all I know
^keep safe^
solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb
Answer:
a = z/mb
Step-by-step explanation:
Given:
[tex]\displaystyle \large{z=mab}[/tex]
To solve for a, divide both sides by the variables mb to isolate a-term.
[tex]\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}[/tex]
Simplify the expression and we finally have solved for a-term.
[tex]\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}[/tex]
Therefore, the answer to this question is a = z/mb.
Please let me know if you have any questions regarding my answer or explanation!
help pls im being timed
The trigonometric ratios show that the angle FHE is 48.59°.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex](hypothenuse)^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:
[tex]sin(\alpha) =\frac{opposite \;leg }{hypotenuse} \\ \\ cos(\alpha) =\frac{adjacent\;leg }{hypotenuse} \\ \\ tan(\alpha) =\frac{sin(\alpha )}{cos(\alpha )}= \frac{opposite \;leg }{adjacent\;leg } \\ \\[/tex]
It is important to remember that the sum of internal angles for any triangle is 180°.
From the question, it is possible to see 2 right triangles (HGF and FHE).
You can find the hypotenuse of the triangle HGF from the trigonometric ratio: sen Θ
[tex]sin45=\frac{opposite\; leg }{hypotenuse} =\frac{\sqrt8}{hypotenuse}\\ \\ \frac{\sqrt{2} }{2} =\frac{\sqrt{8} }{hypotenuse} \\ \\ \sqrt{2}*hypotenuse=2\sqrt{8} \\ \\ hypotenuse=\frac{2\sqrt{8} }{\sqrt{2}} =2\sqrt{4} =2*2=4[/tex]
The hypotenuse of triangle HGF is one of legs for the triangle FHE. The, you can find the angle FHE from the trigonometric ratio: tan β. Thus,
[tex]sin \beta =\frac{opposite\; leg }{adjacent\; leg} =\frac{3}{4}\\ \\ sin \beta=\frac{3}{4}=0.84806\\ \\ arcsin\beta =48.59^{\circ \:}[/tex]
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What is the common ratio for this geometric sequence?
16, 8, 4, 2, ...
One angle of a right-angled triangle is 60 grades . Find the other angle in degree.
Answer:
30°
Step-by-step explanation:
This right triangle has :
right angle (90°)One angle of 60°=========================================================
Solving :
We know the angle sum of a triangle is 180°.
⇒ x + 90° + 60° = 180°
⇒ x + 150° = 180°
⇒ x = 30°
We know the angle sum of a triangle is 180° so
x + 90° +60°= 180°
x + 150°= 180°
⇒x = 30°
________________________________[tex]\boxed{\blue{ » \: Lear \: math \: with \: Kareninajovanka \: « コ:彡}}[/tex]
c) What is the equation of line a? (2 points)
The line a is an illustration of a proportional linear equation, and the equation of line a is y = 1.4x
How to determine the equation of the data?The line a passes through the following points:
(x,y) = (0,0) and (1.3, 1.82(
The above means that line a is a proportional linear equation
The constant of proportionality (k) is calculated using:
k = y/x
Using the values on the table, we have:
k = 1.82/1.3
Divide
k = 1.4
Substitute k = 1.4 in k = y/x
y/x = 1.4
Multiply both sides by 1.4
y = 1.4x
Hence, the equation of the line a is y = 1.4x
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What is the recursive rule for the sequence?
Answer:
2nd option
Step-by-step explanation:
the recursive rule is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( d is the common difference )
use the explicit rule to find a₁ and d
a₁ = 48 - 11(1) = 48 - 11 = 37
a₂ = 48 - 11(2) = 48 - 22 = 26
then
d = a₂ - a₁ = 26 - 37 = - 11
recursive rule is then
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 11
a₁ = 37
Prove (1+tanx)/(1+cotx)=tanx by algebra
[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
11/12 - 7/9
5/36
5/72
25/36
25/72
c
Step-by-step explanation:
10 The length of a piece of wood is 294 cm when truncated to the nearest centimetre. Complete the error interval for the length of the piece of wood.
The error interval for the length of the piece of wood is 293.5 ≤ length < 294.5
What is Error Interval ?Error Interval can be defined as the limit of Accuracy when a number has been truncated.
It is given that the length of the piece of wood is 294 cm truncated to the nearest centimeter.
To determine the error interval for the length of the piece of wood
length ≥ 293.5
length < 294.5
293.5 ≤ length < 294.5
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please help if u know :D
Answer:
B.
Step-by-step explanation:
We can start by dividing 3.5 and 0.75.
3.5/0.75 is 4.67.
Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.
1*4.67 is 4.67.
What is the average rate of change for this function for the interval from x=3 to x=5
The average rate of change is 12 the interval from x=3 to x=5.
How to find the average rate of change of something?Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where when
[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]
Given:
Interval; x = 3 to x = 5
We can represent these by
[tex]x_1 = 3\\x_2 = 5[/tex]
The corresponding y values are as follows
When x = 3, y = 8
When x = 5, y = 32
This will also be represented
[tex]y_1 = 8\\y_2 = 32[/tex]
The average rate of change is then calculated as follows
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\\\m = \dfrac{32 -8}{5-3}\\\\m = \dfrac{24}{2}\\\\m = 12[/tex]
Hence, the average rate of change is 12.
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Find the midpoint of A and B where A has coordinates (8, 2)
and B has coordinates (3,8).
Answer:
(5.5, 5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (8, 2 ) and (x₂, y₂ ) = B (3, 8 ) , then
midpoint = ( [tex]\frac{8+3}{2}[/tex] , [tex]\frac{2+8}{2}[/tex] ) = ( [tex]\frac{11}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = (5.5, 5 )
Your mortgage is a 30-year fixed at 8% on $150,000. you are considering refinancing at 3.5% fixed for 30 years. the bank charges you 1.5% of your debt in closing fees. approximately how long will it take you to recoup the closing fees from the reduced loan payment amount?
ch statement is true about the graphs of the two lines y=-6 and x =
dx= -1/?
The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope that is
ndefined, and the graph of x = is a vertical line with a slope of 0.
The lines are perpendicular to each other because the graph of y=-6 is a vertical line with a slope that is
ndefined, and the graph of x = is a horizontal line with a slope of 0.
The lines are perpendicular to each other because the graph of y = -6 is a vertical line with a slope of 0, and th
aph of x = is a horizontal line with a slope that is undefined.
he lines are perpendicular to each other because the graph of y=-6 is a horizontal line with a slope of 0, and
e graph of x = is a vertical line with a slope that is undefined.
Answer:
IT'S A !
Step-by-step explanation:
Took the quiz on edge 2022 .
the correct statement is:
"The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope."
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Find correct statement is true about the graphs of the two lines y=-6 and x = dx
Since, horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope.
Therefore, the correct statement is:
"The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope."
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Can someone say happy birthday to me do it for how every many point this question is gonna give yoouuu
Answer:
Happy birthday <3
Step-by-step explanation:
:)
Help me please I dont know what the answer is here...
If you can, please write the steps so i can understand better next time.
For this problem, let's think of this shape as a rectangle and a triangle put together. We'll calculate the area of each shape and add them together to get the total area.
For the rectangle, the equation is b*h. Here the base = 7 cm and the h = 4cm
For the triangle, the equation is 1/2 * (b*h). Here the base is a little tricky to find. We know the total length is 12cm and the rectangle length was 7cm. So 12-7= 5cm, which is the base of the triangle. The height would be the same (4cm).
Once you calculate those two areas and add them up, you'll have the total area of this shape.
Determine the value of "a" for which g(h(a)) = 13
Answer:
a = 6
Step-by-step explanation:
g(x) = 5x - 2
h(x) = √(x + 3)
g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2
g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2
5[tex]\sqrt{a+3}[/tex] - 2 = 13
5[tex]\sqrt{a+3}[/tex] = 15
[tex]\sqrt{a+3}[/tex] = 3
( [tex]\sqrt{a+3}[/tex] )² = 3²
a + 3 = 9
a = 6
Uv has endpoints at u(4, 6) and v(10, 4). find the midpoint m of uv.
write the coordinates as decimals or integers.
m =
submit
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ U(\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad V(\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 10 +4}{2}~~~ ,~~~ \cfrac{ 4 +6}{2} \right)\implies \left( \cfrac{14}{2}~~,~~\cfrac{10}{2} \right)\implies (7~~,~~5)[/tex]
What is the value of n?
38°
Answer: 247 the Answer
5. Find the value of x so that lines s and t are parallel.
(7x - 20)°
(4x + 16)
The value of x so that lines s and t are parallel is 12
How to find angles involving parallel lines?The angle are alternate exterior angles.
Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.
Hence,
7x - 20 = 4x + 16
7x - 4x= 16 + 20
3x = 36
x = 36 / 3
x = 12
Therefore, the value of x is 12.
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What equation has the same solution as 3x-5=5x + ll
Answer: -5=2x+11
Step-by-step explanation:
3x-5=5x+11
subtract 3x to both sides
3x-5 - 3x =5x+11 - 3x
simplify
-5 = 2x +11
answer is -5=2x+11
A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?
Zane works for a catering company and is bringing a total of 160 servings of food to a conference. If 40 people come to the conference, there would be enough for each person to have 4 servings of food. If 80 people come to the conference, there would be enough for each person to have 2 servings of food.
Does this situation represent an indirect variation? If so, what are the independent and dependent variables?
A.
No, this is not an indirect variation. The product of the variables is not constant.
B.
Yes, this is an indirect variation. The number of servings per person is the independent variable, and the number of people is the dependent variable.
C.
Yes, this is an indirect variation. The number of people is the independent variable, and the number of servings per person is the dependent variable.
D.
Yes, this is an indirect variation. However, because the number of people is undetermined, the variables cannot be determined.
Answer:
D
Step-by-step explanation:
Since we don't know how many people we don't know how many servings would be consumed. therefore this is an indirect variation
TIME SENSITIVE!!! What will the first row of this multiplication be? (first image is the problem, second is the options)
Answer:
the first option
Step-by-step explanation:
hope the answer helps...
Which equation can be solved by using this system of equations?
StartLayout Enlarged left-brace 1st Row y = 3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 2nd Row y = 4 x Superscript 4 Baseline + 6 x cubed minus 11 EndLayout
The equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
How to determine the equation?The correct formats of the equations are:
y = 3x^5 - 5x^3 + 2x^2 - 10x + 4
y = 4x^4 + 6x^3 - 11
To determine the equation, we substitute 4x^4 + 6x^3 - 11 for y in the first equation.
So, we have:
4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
Hence, the equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
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Is b=2a+10 equal to 4a+2b=10
Answer:
Yes
Step-by-step explanation:
You are packing for a road trip and you buy snack packages (same size, same weight) for the trip. you buy 6 potato chips, 5 doritos, and 3 corn curls. you put them in a bag and mix them up. during the trip, you reach into the bag and pull out two packages at random, one at a time. draw a tree and calculate the probability of each outcome. use p for potato chips, d for doritos, and c for corn curls. what is the probability of picking two snacks of the same type?
The probability of picking two snacks of the same type is 0.308.
How to calculate the probability?The probability of picking 2 potato will be:
= 6/14 × 5/13
= 0.429 × 0.385
= 0.165
The probability of picking 2 doritos will be:
= 5/14 × 4/13
= 0.357 × 0.308
= 0.110
The probability of picking 2 corn curls will be:
= 3/14 × 2/13
= 0.214 × 0.154
= 0.033
Therefore, the probability of picking two snacks of the same type will be:
= 0.165 + 0.110 + 0.033
= 0.308
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HELP ME PLSSS
A rectangle has a height of 4 and a width of x² + 3x + 2.
Express the area of the entire rectangle.
The area of the entire rectangle is 4x² + 12x + 8
How to determine the area of the entire rectangle?The given parameters are:
height = 4
Width = x² + 3x + 2
The area of the rectangle is:
Area = Width * Height
So, we have:
Area = (x² + 3x + 2) * 4
Expand
Area = 4x² + 12x + 8
Hence, the area of the entire rectangle is 4x² + 12x + 8
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