Answer:
-(x + 3)(x - 3)
Step-by-step explanation:
Using the difference of squares we can factor this expression.
[tex](9 - x^2)\\= (3^2 - x^2)\\= (3 + x)(3 - x)\\= -(3 + x)(-3 + x)\\= -(x + 3)(x - 3)[/tex]
Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?
∠P
∠Q
∠T
∠U
Answer:
[tex]\angle P[/tex]
Step-by-step explanation:
Given
[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]
[tex]PQ = 20[/tex] [tex]QR = 16[/tex] [tex]PR = 12[/tex]
[tex]ST = 30[/tex] [tex]TU = 34[/tex] [tex]SU = 16[/tex]
See attachment
Required
Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]
Considering [tex]\triangle PQR[/tex]
We have:
[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse
So, we have:
[tex]\sin(P) = \frac{16}{20}[/tex]
Divide by 4
[tex]\sin(P) = \frac{4}{5}[/tex]
Hence:
[tex]\angle P[/tex] is correct
Answer:
A or <P
Step-by-step explanation:
on edge 2021
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
To make concrete, the ratio of cement to sand is 1 : 3. If cement and sand are sold in bags of equal mass, how many bags of cement are required to make concrete using 15 bags of sand?
Answer:
5 bags of cement are required.
Step-by-step explanation:
Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:
Cement = 1
Sand = 3
3 = 15
1 = X
15/3 = X
5 = X
Therefore, 5 bags of cement are required.
The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
To solve more questions on expressions, visit the link below -
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Look at the numbers below. −9.8 −5.4 1.0 14.8 Which shows the best way to add these numbers using the Commutative and Associative Properties? A. (–9.8 + 1.0) + (–5.4 + 14.8) B. (–9.8 + 14.8) + (–5.4 + 1.0) C. (1.0 + 14.8) + (–9.8 + (–5.4)) D. (1.0 + (–9.8)) + (14.8 + (–5.4)
Answer:
B
Step-by-step explanation:
i did the test and it was correct, ur welcome
Riley wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 4.5% and the other bank is offering a rate of 4.5% compounded annually. Which is the better deal?
Peter, Jan, and Maxim are classmates. Their total score for the last test was 269. Peter's score was more than the sum of Jan's and Maxim's scores. What could be Peter's least possible score?
Answer:
135
Step-by-step explanation:
Given that :
Total score obtained by Peter, Jan and Maxim = 269
Let :
Peter's score = x
Jan's score = y
Maxim's score = z
x + y + z = 269
x > (y + z)
For x to be greater Than y + z ;
Then x > (269 / 2) ; x > 134.5
The least possible x score is 135
Hence, Peter's least possible score is 135.
A half-century ago, the mean height of women in a particular country in their 20s was inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of of today's women in their 20s have mean heights of at least inches?
Answer:
0.26684
Step-by-step explanation:
Given that :
Mean, μ = 62.5
Standard deviation, σ = 1.96
P(Z ≥ 63.72)
The Zscore = (x - μ) / σ
P(Z ≥ (x - μ) / σ)
P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)
P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)
1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684
9. Which is a true statement about the denominator in a fraction?
(Select one answer)
It is always a negative number
It cannot be 0
It has to be an even number
It is always smaller than the numerator
Answer:
It cannot be 0
Step-by-step explanation:
it can also be positive number :2/4
it can be odd number too:3/9
it is bigger than numerator bcoz we have to divide it for numerator
So, 0 number cannot be put as denominator in fraction is true statement
Evaluate −a2+c2 when c=−4.
Answer:
[tex]a = 4, -4[/tex]
Step-by-step explanation:
Step 1: Plug in -4 for c
[tex]-a^{2} + c^{2}[/tex]
[tex]-a^{2} + (-4)^{2}[/tex]
[tex]-a^{2} + 16[/tex]
Step 2: Solve for a
[tex]-a^{2}+16-16=0-16[/tex]
[tex]-a^{2}/-1 = -16/-1[/tex]
[tex]a^{2} = 16[/tex]
[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]
[tex]a = 4, -4[/tex]
Answer: [tex]a = 4, -4[/tex]
What type of object is pictured below?
O A. Point
O B. Ray
C. Segment
D. Line
Answer:
It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.
A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy a rectangular pool that is 20' x 15' in 54 inches deep or a cylindrical pool that has a 3.3 m radios and is 1.8 m deep
Answer:
20'×15 in 54 inches
Step-by-step explanation:
The Best as a pool should be rectangular in shape and 54inches deep for safety of life's
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2}[/tex]h
The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;
= [tex]\pi r^{2}[/tex]h
[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]
The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;
V = 20 x 15 x 54
V = 16,200 cubic meter.
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
Learn more about volume;
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Find the slope, if it exists, of the line containing the points (10,-3) and (10,-8).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
m=
Answer:
The slope is undefined.
Step-by-step explanation:
The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order DE y' = y − y2. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(0)=-1/3
If y (0) = -1/3, then
-1/3 = 1 / (1 + C e ⁻⁰)
Solve for C :
-1/3 = 1 / (1 + C )
-3 = 1 + C
C = -4
So the particular solution to the DE that satisfies the given initial condition is
[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]
What is the area of the shaded part of the figure?
Answer:
14cm²
Step-by-step explanation:
3x2=6,
3x2=6,
2x1=2,
6+6+2=14 cm^2
Find the intersection of the parabola y=-2x^2-4x+2 and the line -6x+y=14
Answer:
(-2,2) and (-3,-4)
Step-by-step explanation:
by graphing the line and parabola, you should get this graph
Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express a simplified ratio
Answer:
5:12
Step-by-step explanation:
125:300 simplified = 5:12
I hope this helps
use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
Use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in cost.
Function x-Value
C=0.025x^2 + 3x + 4 x=10
dC= ___________
ΔC= __________
Answer:
dC=3.5
DC is between 3.475 and 3.525
Step-by-step explanation:
So let dx=1 since the change there is a change in 1 unit.
Find dC/dx by differentiating the expression named C.
dC/dx=0.05x+3
So dC=(0.05x+3) dx
Plug in x=10 and dx=1:
dC=(0.05×10+3)(1)
dC=(0.5+3)
dC=3.5
Let D be the change in cost-the triangle thing.
Since dx=1 we only want the change in unit to be within 1 in difference.
So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.
Let's do from x=9 to x=10 first:
DC=C(10)-C(9)
DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]
DC=[2.5+30+4]-[0.025×81+27+4]
DC=[36.5]-[2.025+31]
DC=[36.5]-[33.025]
DC=3.475
Now let's do from x=10 to x=11
DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]
DC=[0.025×121+33+4]-[36.5]
DC=[3.025+37]-[36.5]
DC=[40.025]-[36.5]
DC=3.525
So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.
Which expression is equivalent to 7x , if b > 0?
Work Shown:
[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]
So that's why the answer is choice C
The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.
Answer:
C.
Step-by-step explanation:
7x²×sqrt(2x⁴)×6×sqrt(2x¹²)
we see right away that as constant multiplication factor we have 7×6 = 42.
and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.
the only answer option with 84 is C.
now, to be completely sure, and to get some practice, let's look at the other parts :
sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²
sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶
=>
7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰
perfect. C is confirmed.
Use the figure to find y.
Tanθ =sin /cos
tan θ = 5/2 / y
tan (30°) = 5/2 /y
[tex]y = \frac{5 \sqrt{3} }{2} [/tex]
y=4.33
The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height
Answer:
21 kilometers
Step-by-step explanation:
Let the height be [tex]x[/tex]. Then, the length of the base is [tex]2x[/tex]. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to [tex]\frac{x \cdot 2x}{2} = x^2[/tex], which is in turn equal to 441. Since [tex]x[/tex] must be positive, then [tex]21^2=441[/tex], meaning that the height is [tex]21[/tex] kilometers.
Which equation could represent a linear combination of the systems?
9514 1404 393
Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
convert 2m 50cm 15mm in cm
Answer:
251.5 cm
Step-by-step explanation:
1 m = 100 cm
1 cm = 10 mm
2 m + 50 cm + 15 mm =
= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)
= 200 cm + 50 cm + 1.5 cm
= 251.5 cm
Find the value of x on this triangle
Answer:
33
a2+b2 =c2
a2+ 33 squared = 55 squared
a + 1936 = 3025
3025-1936=1089
square root of 1089 is 33
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This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
Find x and explain how you found x
Answer:
x=60
Step-by-step explanation:
There are different ways to find x but this is what I found easiest.
To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.
Find the value of x in each case and give an explanation plzzz, thank youu :)
Answer:
Step-by-step explanation:
the arrows from the picture tells us that TV is parallel to RS
since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x
(alternate interior angles)
sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°
2x = 45*2 = 90°
How
many solutions are there to the equation below?
4(x - 5) = 3x + 7
A. One solution
B. No solution
O C. Infinitely many solutions
SUB
Answer:
A one solution
Step-by-step explanation:
4(x - 5) = 3x + 7
Distribute
4x - 20 = 3x+7
Subtract 3x from each side
4x-3x-20 = 3x+7-3x
x -20 = 7
Add 20 to each side
x -20+20 = 7+20
x = 27
There is one solution
Answer:
Step-by-step explanation:
Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.
4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:
1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
