The opposite sides PQ and RS of the parallelogram PQRS are congruent
The value of the length QS is 6 cm
How to determine the length QS?The given parameters are:
PQ = 4x - 1
RS = 3x + 7
Opposite sides are congruent.
So, we have:
4x - 1 = 3x + 7
Collect like terms
4x - 3x = 1 + 7
Evaluate the expressions
x = 8
The perimeter is calculated using:
Perimeter = 2(QS + RS)
This gives
2(QS + RS) = 74
Divide by 2
QS + RS = 37
Substiute RS = 3x + 7
QS + 3x + 7 = 37
Substitute 8 for x
QS + 3*8 + 7 = 37
This gives
QS + 31 = 37
Subtract 31 from both sides
QS = 6
Hence, the value of the length QS is 6 cm
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Answer:
6cm or b
Step-by-step explanation:
In which number is the value of the 7 ten times the value of the 7 in the number 17,862
Answer:
Your answer would require a 7 in the hundreds place
Step-by-step explanation:
A rectangle has a perimeter of 20 cm. What will the perimeter be if the rectangle tripled in size?
ITS A VOLUME QUESTION
Answer:
Step-by-step explanation:
Holding the perimeter fixed, the shape with greatest area is square ( all sides of the same) length) For your name example a square with a perimeter of 20 cm has sides of 5 cm and area of 5 times 4=20 cm) ^3 hope this helps
R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.
Answer:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Step-by-step explanation:
If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.
[tex]\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)[/tex]
[tex]\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)[/tex]
[tex]\sf =(-2, 2)[/tex]
Equation of a circle: [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the center and r is the radius)
Substituting found center (-2, 2) into the equation of a circle:
[tex]\sf \implies (x-(-2))^2+(y-2)^2=r^2[/tex]
[tex]\sf \implies (x+2)^2+(y-2)^2=r^2[/tex]
To find [tex]\sf r^2[/tex], simply substitute one of the points into the equation and solve:
[tex]\sf \implies (-3+2)^2+(1-2)^2=r^2[/tex]
[tex]\sf \implies 1+1=r^2[/tex]
[tex]\sf \implies r^2=2[/tex]
Therefore, the equation of the circle is:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Find a function for the graph below.
a. f(t) = 3 cos 41
b. ft) = 8 sin 3t
fit) = 3 sin 41
d. (t) = 3 cos 6
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The given function has Amplitude of 3, and by seeing it we can conclude that it's a sine function.
Therefore, we can conclude that the required Answer is ~
[tex]\qquad \sf \dashrightarrow \:c. \: f(t) = 3 \sin(4t) [/tex]
The sinusoidal function is represented as y = 3 sin 4t. Then the correct option is C.
What is a sinusoidal Function?It is a function that repeats itself in a particular time interval.
The sine function is given as
y = A sin (wt + Ф)
where A is the amplitude, w frequency, and Ф is the phase difference.
From the graph, the value of the amplitude will be 3, the frequency will be 4, and the phase difference will be 0. Then the equation will be
y = 3 sin4t
More about the sine function link is given below.
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In the following diagram,
A
∥
B
.
Use complete sentences to explain how the special angles created by the intersection of
A
and
B
by
D
can be used to solve for
x
.
Solve for
x
, showing all of your work.
Find the measure of
∠
6
.
Answer:
x=24
<6=79°
Step-by-step explanation:
We can see that if we add 3x+7 and 4x+5, it will total a 180-degree angle. This allows us to solve for x. 3x+7+4x+5=180 7x+12=180 7x=180-12 7x=168 x=24 We can also see that angle six is the same as the angle 3x+7. Since we know x=24, we can solve for those angles. 3(24)+7= 72+7=79 So <6=79 degrees
Please help 8, 9, and 10 you don't need to explain
Answer:
8.
x
12
9
4.5
9.
3, 4, 12
3, 3, 12
6, 12
-6, -12
2
10.
plug in x to check work
Step-by-step explanation:
8.
1/2(x + 24) = 21
1/2x +12 = 21
1/2x = 9
x = 18
9.
28 - 3x - 4 = 2x + 12 + x
24 - 3x = 3x + 12
24 - 6x = 12
-6x = -12
x = 2
10.
3x - 18 + 6 = 5x - 6
3x - 12 = 5x - 6
-2x - 12 = -6
-2x = 6
x = -3
hope it help.
can you answer my question, i can help you in math, can you help me in english? please
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
54
Step-by-step explanation:
Multiply:
37x37=72
Subtract:
180-72=108
Divide:
108/2=54
Answer:
143 degrees
Step-by-step explanation:
37(2) + 2x = 360
74 + 2x = 360
2x = 286
x = 143
Hope this helps :)
What is the median of this data set?
{13, 13, 13, 15, 15, 16, 16, 17, 17}
{13, 13, 13, 15, 15, 16, 16, 17, 17}
the median is 15
Answer:
it is 15.
Step-by-step explanation:
the median is the middle number in the data set. in this case, 15 is in the middle.
Find the measures of the interior angles?
Answer:
well it's says for a its 35° and B is 100° to find x it would be 180-(35+110)=x
Step-by-step explanation:
180-(35+110)=180-145=35. so x=35°
Trigonometric Equations
Solve the equation over the interval [0°, 360°)
2sin^2theta-5sintheta+3=0
Step-by-step explanation:
The solutions are
S
=
{
30
º
,
150
º
,
270
º
}
Explanation:
The equation is
2
sin
2
θ
+
sin
θ
−
1
=
0
We can factorise the LHS
(
2
sin
θ
−
1
)
(
sin
θ
+
1
)
=
0
Therefore,
sin
θ
=
−
1
,
⇒
,
θ
=
270
º
sin
θ
=
1
2
,
⇒
,
θ
=
30
º
,
150
º
When do you say that a given quadrilateral is a parallelogram?
Answer:
If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D. We know that the sum of the angles of a quadrilateral is 360o.
Step-by-step explanation:
hope that helps
y by the power of 2 + 4=20
Answer:
y is equal to 4 if that's what ur asking for
Answer:
16 if ur asking for y^2+4=20
Step-by-step explanation:
A bag has 16 blue marbles and 14 red marbles. John will randomly select 1 marble from the bag. What is the probability that he will select a red marble? *
Answer:
46.66% chance of red marble
Step-by-step explanation:
Red Marbles / Total Marbles gives you the percent
14 / 30 = 46.66%
If a puzzle measures 14 in x 16 in, how many inches of frame for the puzzle?
Nine more than the product of a number and eight equals four
Answer:
Step-by-step explanation:
Let the number = 'x'
Product of number and eight ⇒ 8*x = 8x
Nine more than the product of 8x ⇒add 9 to 8x
8x + 9 = 4
8x = 4 - 9
8x = -5
x = -5/8
A rare species of insect was discovered in the rain forest. In order to protect the species,
environmentalists declare the insect endangered and transplant the insects into a protected area.
The population of the insect t months after being transplanted is given by P(t).
P(t) =
60(1+0.4)
0.01t+3
a. How many insects were discovered? In other words, what was the population when t = 0?
b. What will the population be after 5 years? Round to the nearest whole insect.
Using the given function, it is found that:
a) 20 insects were discovered.
b) The population after 5 years will be of 417 insects.
What is the function for the number of insects after t months?As stated in the exercise, it is given by:
[tex]P(t) = \frac{60(1 + 0.4t)}{0.01t + 3}[/tex]
Item a:
[tex]P(0) = \frac{60[1 + 0.4(0)]}{0.01(0) + 3} = \frac{60}{3} = 20[/tex]
20 insects were discovered.
Item b:
5 years = 60 months, hence:
[tex]P(60) = \frac{60[1 + 0.4(60)]}{0.01(60) + 3} \approx 417[/tex]
The population after 5 years will be of 417 insects.
More can be learned about functions at https://brainly.com/question/25537936
y=5/2x-9 find the y intercept
Answer:
(0,-9) You have to substitute 0 for x and solve for y
Abdul is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular prism. He now needs to cover the wooden blocks on all sides with a green fabric.
How much fabric does Abdul need in order to cover 8 of these blocks?
Step-by-step explanation:
4cm×2cm×1/2=4cm³
4cm³×8=32cm³
I think the answer is 176
Step-by-step explanation:
please tell me if I'm wrong
can you please help me
Answer:
168
Step-by-step explanation:
yea..
A company wants to decrease their
energy use by 15%. If their electric
bill is currently $2,100 a month,
what will their bill be if they are
successful? Give your answer
accurate to at least the nearest
dollar.
15% decrease means the bill would be 85% of the original bill ( 100% -15% = 85%)
multiply the current bill by 85%
2100 x 0.85 = 1.785
the bill would be $1,785
The field trip to the science museum will cost $22 per student. If Mrs. Robertson has 24 students, how much money will she collect in all?
Answer:
528
Step-by-step explanation:
22x24=528
Answer:528$
Step-by-step explanation: you have to do 22 dollars times 24 students which would be 528
11. Determine whether the events are independent or dependent. Explain your answer.
(3 points each)
a. Randomly choosing an oatmeal cookie, eating it, and then choosing a peanut butter
cookie from a container of cookies.
b. Drawing the name "Sally" from a hat and replacing it, and then drawing the name
"Malcolm" from the hat.
The fact that one chooses an oatmeal cookie, eating it and then choosing a peanut butter cookie from a container of cookies is an independent event.
What is a dependent event?It should be noted that dependent events influence the probability of the other events.
In this case, the fact that one chooses an oatmeal cookie, eating it, and then choosing a peanut butter cookie from a container of cookies is an independent event.
On the other hand, drawing the name "Sally" from a hat and replacing it, and then drawing the name "Malcolm" from the hat is a dependent event.
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Express 9 2/3 out of 100 as a percent .
Answer:
9 2/3% (or 9.66666666666%)
Step-by-step explanation:
A percent is a ratio out of 100, as this answer is out of 100, the percent is just 9 2/3%.
Find the midpoint of BF B(0,-14) F(4,6)
Answer:
Step-by-step explanation:
B(0, -14) ⇒ x₁ = 0 & y₁ = -14
F(4,6) ⇒ x₂ = 4 & y₂ = 6
[tex]Midpoint = \left(\dfrac{x_{1}+x_{2}}{2}, \dfrac{y_{1}+y_{2}}{2} \right)[/tex]
[tex]=\left(\dfrac{0+4}{2},\dfrac{-14 + 6}{2}\right)\\\\\\= \left(\dfrac{4}{2}, \dfrac{-8}{2} \right)\\\\\\=\left(2, -4 \right)[/tex]
A light bulb's brightness is reduced when placed behind a screen. The amount of visible light produced by the light bulb decreases by 25% with each additional layer that is added to the screen. With no screen, the light bulb produces 750 lumens. The lumen is a unit for measuring the total quantity of visible light emitted by a source.
Select the correct equation that can be used to represent the lumens, L, after x screen layers are added.
A.
L = 750(1.25)x
B.
L = 750(0.75)x
C.
L = 750(0.975)x
D.
L = 750(0.25)x
Answer:
b
Step-by-step explanation:
The required equation that can be used to represent the lumens, L, after x screen layers are added is [tex]l = 750(0.75)^x[/tex]. Option B is correct.
What is the equation?The equation is the relationship between variables and is represented as y = ax+ v an example of a polynomial equation.
Let L be the power of the bulb in lumens and x be the number of layers added to the screen. Since every layer decreases the brightness of the blubs by 25%, The sequence in which the light brightness gets decreased.
For number of screen x = 1
= 750(1 - 0.25)
For number of screen x = 2
= 750(1 - 0.25)(1 - 0.25)
For number of screen x = 3
=750(1 - 0.25)(1- 0.25)(1-0.25)
.... so on
The above observation can be computed as power (1 - 0.25) increasing after adding a number of screens,
Now
[tex]L = 750(1 - 0.25)^x\\L = 750(0.75)^x[/tex]
Thus, The required equation that can be used to represent the lumens, L, after x screen layers are added is [tex]l = 750(0.75)^x[/tex].
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3 times the age of Felicia is 4 more than the age of Asare.in 3 years,the sum of their ages will be 30 years,find their present age
Answer:
Asare is 17 and Felicia is 7.
Step-by-step explanation:
let x be felicia's current age and y be asare's age. The equation for their age is y=3x-4. If 3x-1 + x+3 = 30, that means that 4x+2=30, so 4x=28. If 4x=28, x=7. Felicia is 7 and 3*7-4=17.
PLEASE HELP ME PLEASE
Answer
true
Step-by-step explanation:
Answer:
I think true because that's the only star that is closest to the earth
Please help!! I will give brainliest :)
Answer: I think its 75 percent
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
The shaded is part of the poster 9/12
To convert 9/12 into a percent
100 ÷ 12 = 8.3333333333333
[tex]\frac{9*8.3333333333}{12*8.3333333333} = \frac{75}{100}[/tex]
label the angle that is 57° in this 2-dimensional figure.
The measure of the angle that is 57° in this 2-dimensional figure is the angle vertically opposite to the angle 57 (the angle formed at X)
Line and anglesFrom the given diagram, we have the following:
The two angles on the straight line are 123 degrees and 57 degrees.
<F + 57 = 180
<F = 180 - 57
<F = 123 degrees
Hence the measure of the angle that is 57° in this 2-dimensional figure is the angle vertically opposite to the angle 57 (the angle formed at X)
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Find the missing side lengths. Leave your answers as radicals in simplest form.
1)
2)
1459
712
b
b
र
45°
a
X
3)
D)
X
у
45 6/3
459
912
X
x
Answer:
1) y = 7 x = 7
2) y = 4.243 x = 4.243
3) y = 7.348 x = 7.348
4) y = 9 x = 9
Step-by-step explanation:
just use a calculator and put in the given information
search Right Triangle Side and Angle Calculator
Answer:
Below in bold.
Step-by-step explanation:
1. This is an isosceles right angled triangle.
x = y.
The ratio of the sides in this triangle are 1:1:√2
So 1/√2 = x / 7√2
√2 x = 7√2
x = 7.
y = 7.
The other 3 are solved in a similar way as they are all isosceles right angled triangles:
2. b = 6 and a = 6√2.
3. 1 / √2 = x / 6√3
√2 x = 6√3
x = 6√3 / √2
x = 6√3 * √2 / 2
= 3√6
y = 3√6.
4. x = y = 9.