Answer:
x = 3t/b
Step-by-step explanation:
Step 1: Multiply both sides by 3
t = bx/3
3t = bx
Step 2: Divide both sides by b
3t/b = x
The segments shown below could form a triangle.
Answer: B. False
Step-by-step explanation:
It does not follow the Pythagorean Theorem (a^2 + b^2 = c^2)
The sum of the two legs (shorter sides) squared would have to equal the hypotenuse (longest side) squared in order to form a right triangle.
5^2 = 25
6^2 = 36
25 + 36 = 61
8^2 = 64
61 < 64
*One half of two fifths of x.
Answer:
one half of two fifths of x would be equivalent to one fifth of x
You and your business partner track the number of customers served and the amount of tips collected per day. The data you gathered is displayed in the chart below. Servers’ Collected Tips Customers 54 46 34 67 52 22 49 64 55 80 38 42 Tips ($) $92 $80 $76 $121 $109 $43 $87 $114 $99 $174 $88 $91 a) Create a scatterplot displaying the data in the table. Be sure to include a linear trend line
Answer:
Simply create a scatter plot then write in a line of best fit.
Step-by-step explanation:
Answer:
create a scatter plot then write in a line of best fit.
Step-by-step explanation:
1.)The angle θ lies in Quadrant IV. sinθ=−2/3 What is cosθ?
a. −2/3
b. 2/3
c. −5/√3
d.5/√3
2.)The angle θ lies in Quadrant I. cosθ=3/5 What is tanθ?
a.4/3
b.−4/5
c. −4/3
d. 4/5
3.)Given sin(−θ)=−1/6 and tanθ=−35/√35. What is the value of cosθ?
a.−35/√210
b.−35/√6
c.35/√210
d.35/√6
4.)cos(−θ)=3/√4, sinθ<0 What is the value of sinθ?
a.13/√4
b. 13/√16
c. −13/√16
d.−13/√4
5.)Marty is proving that the following trigonometric identity is true: tan^2 θ⋅cos^2 θ=1−cos^2 θ
Which step would be the first line of his proof?
a. tan^2 θ⋅cos^2 θ=tan^2 θ
b. tan^2 θ⋅cos^2 θ=sin^2 θ
c.tan^2 θ⋅cos^2 θ=1−sin^2 θ
d.tan^2 θ=1−cos^2 θ⋅cos^2 θ
Answer:
1. From sin²θ +cos²θ =1 and sinθ=-2/3, we see that cosθ=√(1-sin²θ) or cosθ=√5/3, where the sign of cosine is positive as it is in Quadrant IV. x lies in 4th quadrant , cos x is +ve. , cos x = √5/3. Answer.
answer : cos x = √5/3
2. 4/3
3. sin (- theta) = - sin (x) so sin x = 1/6
tan = sin / cos = 1/6 / cos = - sqrt35/35 solve for cos
cos = 1/6 * (-35/sqrt35)
= -35 sqrt35 /210
answer : −35/√210
4. The cosine function is an even function, so cos(θ) = cos(-θ).
The relationship between sin(θ) and cos(θ) is sin(θ) = ±√(1 -cos(θ)^2)
For sin(θ) < 0 and cos(θ) = (√3)/4, sin(θ) = -√(1 -3/16) = -√(13/16)
sin(θ) = -(√13)/4 For sin(θ) < 0 and cos(0) = √(3/4), ...
sin(θ) = -√(1 -3/4) = -√(1/4) sin(θ) = -1/2
answer : -13/√4
5. answer : tan^2 θ ⋅ cos^2 θ = 1 − cos^2 θ would be the first step
Help help urgentlyyy please❤️❤️
Answer:
g(2) = 5
g(-2) = 2
g(-3) = 0
g(5) = 1
g(x) = 0 when x = 3
g(x) = 6 when x = 0
Step-by-step explanation:
Your just finding the values of y when x is unknown or when y is unknown and your trying to find x. f(x) is just a fancy way of saying y.
What is the value of this expression when g=-3.5?
8-12g-51
Step-by-step explanation:
If g=3.5 what about 12g
12g×3.5=42
8_42_51=_85
Given: x + 2y=-6.
Solve for y
Oy=x-6/2
Oy=-x+6/2
Oy=-x-6/2
Answer:
y = (-x - 6)/2
Step-by-step explanation:
x + 2y = -6
2y = -x - 6
y = (-x - 6)/2
Please help! Segment QR is tangent to circle P at point Q. What is the measure of angle PQR? A.) 37 degrees B.) 53 degrees C.) 90 degrees D.) 97 degrees
Answer:
Correct option: C) 90 degrees
Step-by-step explanation:
When we have a tangent segment to a circle, the angle made with the radius of the circle and the tangent segment is always a right angle, that is, 90 degrees. In other words, the radius and the tangent segment are always perpendicular.
If QR is tangent to the circle P, and PQ is the radius of the circle, the segment PQ is perpendicular to the segment QR, so the angle PQR is equal 90 degrees.
Correct option: C)
Answer:
Angle PQR is 90 so answer would be C
Step-by-step explanation:
Given 1 ABCD and 2D = 1459, what is the measure of C?
A. 1450
B. 900
C. 105°
D. 35°
E. 80°
F. Cannot be determined
Answer:
D
Step-by-step explanation:
Assuming the figure to be a parallelogram, then
The consecutive angles are supplementary, that is
∠ D + ∠ C = 180°
145° + ∠ C = 180° ( subtract 145° from both sides )
∠ C = 35° → D
A $86 ,000 trust is to be invested in bonds paying 9% , CDs paying 6% , and mortgages paying 10% . The bond and CD investment together must equal the mortgage investment. To earn a $7180 annual income from the investments, how much should the bank invest in bonds?
Answer:
to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.
Step-by-step explanation:
Let the mortgage investment be X
The Bond to be Y
and the CDs to be Z
Thus;
X+Y+Z = 86000 ------- (1)
Y + Z = X ------------(2)
10X + 9Y + 6Z = 7180 × 100 ------ (3)
So;we now have:
X+Y+Z = 86000 ------- (1)
Y + Z = X ------------(2)
10X + 9Y + 6Z = 718000 ------ (3)
Let ; replace X with Y+Z in equation (1) and (3)
Y+Z + Y+Z = 86000
2Y + 2Z = 86000
Divide both sides by 2
Y+Z = 43000 ------ (4)
From equation (3)
10X + 9Y + 6Z = 718000
10(Y+Z) + 9Y + 6Z = 718000
10Y +10Z + 9Y +6Z = 718000
19Y + 16Z = 718000 -----(5)
Y+Z = 43000 ------ (4)
19Y + 16Z = 718000 -----(5)
Using elimination method; multiply (-16) with equation (4) and (5) ; so, we have:
-16 Y -16 Z = -688000
19Y + 16Z = 718000
3Y + 0 = 30000
3Y = 30000
Y = 30000/3
Y = 10000
From (4);
Y+Z = 43000
So; replace Y with 10000; we have:
10000 + Z = 43000
Z = 43000 - 10000
Z = 33000
From (1) ;
X+Y+Z = 86000
X + 10000 + 33000 = 86000
X + 43000 = 86000
X = 86000 - 43000
X = 43000
Since we assume the bond to be Y and Y = $10000;
Thus; to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.
The Goodsmell perfume producing company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to hold at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and he corresponding surface are and volume.
Answer:
Dimensions of the bottle
x (radius of the base ) = 3,99 cm
h (heigh of the bottle ) = 3,99 cm
Surface area = 149,99 cm²
Volume of the bottle = 199,45 cm³
Step-by-step explanation:
The bottle volume must be V(b) = 100 ml or V(b) = 100 cm³
The shape of the bottle is cylindrical
Surface area of bottle is
S = surface area of the base + lateral area
Area of the base = π*x ² where x is radius of circle
Lateral area is 2*π*x*h where h is the heigh of the bottle
V(b) = π* x²*h (1)
π*x² + 2*π*x*h < 150 cm² we work with the limit 150
π*x² + 2*π*x*h = 150
h = (150 - π*x²) /2*x*π
Plugging that value in equation (1)
V(x) = π*x² * (150 - π*x²) /2*x*π ⇒ V(x) = 150*π*x²/2*x*π - π²*x⁴/2*x*π
V(x) = 75*x - π*x³/2
Taking derivatives on both sides of the equation
V´(x) = 75 - 3*π*x²/2
V´(x) = 0 75 - 3*π*x² /2 = 0
x² = 75*2 /3*π ⇒ x² = 15,92 ⇒ x = 3,99 cm
And h = ( 150 -π*x² )/2*π*x
h = ( 150 - 49,98 )/25,05
h = 3,99 cm
Dimensions of the bottle
x (radius of the base ) = 3,99 cm
h (heigh of the bottle ) = 3,99 cm
Surface area = 149,99 cm²
Volume of the bottle = 199,45 cm³
can you solve - x/4<7 ?
Answer:
Step-by-step explanation:
A band went to a recording studio and recorded 4 songs in 3 hours. How many hours would it take the band to record 9 songs if they record at the same rate?
Answer:
6 hours and 45 minutes
Step-by-step explanation:
if you divide 3 hours by four songs you deduce that it take 45 minutes to record one song.
8 is double 4 so it will take 3more hours plus the 45 minutes for the ninth song.
3+3+.45= 6.45
A windshield wiper blade is 18 inches long. To the nearest square
inch, what is the area covered by the blade as it rotates through an
angle of 122 degrees? (Enter just a number for your answer.)
the answer is 22 degrees
The area covered by the blade as it rotates through an angle of 122 degrees is approximately 346 square inches.
We have,
The area of a sector can be calculated using the formula:
Area = (θ/360) * π * r²
where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sector.
The central angle is 122 degrees, and the radius of the wiper blade is 18 inches.
Substituting the values into the formula:
Area = (122/360) * π * (18²)
Area = (0.3389) * 3.14159 * 324
Area ≈ 344.77 square inches
Area = 345 square inches
Therefore,
The area covered by the blade as it rotates through an angle of 122 degrees is approximately 346 square inches.
Learn mroe about the area of sectors here:
https://brainly.com/question/1582027
#SPJ4
What is the perimeter of quadrilateral ABCD?
3+
O 18 + 2 units
A(-3,2)
B (42)
2
O 18 + 6 units
54 -2 -1
O 18 + 26 units
1 2 3 4 5
O 18 + 50 units
C (3.-3)
Answer:
I believe it is 18 + the square root of 26.
Step-by-step explanation:
The slope of line BC should be 5/1 because it goes up 5 times and to the right once. If you square root 26 you get 5.09.
Basil asks each of 40 students how many books they bought last year. Can anyone answer B?
Answer:
10 books.
Step-by-step explanation:
(b) To estimate the mean we take the mean value of books for each bar.
So for 0-4 books we use 4/2 = 2, for 5-9 we use (9-5)/ 2 + 5 = 7 and so on for each bar. So the estimate for the first bar is 2 * 9 = 18 books.
So the required mean = total estimate of books bought / number of students
= (9 *2 + 10*7 + 12*13 + 17*2 + 22*6) / 40
= 410 / 40
= 10.25
any number that divisible by 3 is also divisible by 6 . Find a counterexample to show that the conjecture is false
Answer:
Counterexample: 21 which is divisible by 3 but not by 6.
Step-by-step explanation:
Use for example the number 21 which is divisible by 3 rendering 7, but not divisible by 6.
You can find any number with at least a factor of "3", but no factor "2" in it, so any odd number divisible by 3 would work as counterexample.
The amount of time (t) in minutes it takes to make a coffee at Starbucks is related to (n) the number of coffees they purchase. The equation is t= 21-3 How long does it
take if a customer buys 5 coffees?
Answer: 7 minutes
Step-by-step explanation:
There is no n variable in the question, found the original question and the equations is: t = 2n – 3.
So, to answer this question we simply have to substitute n=5 in the equation given:
t = 2(5) – 3.
Solving for t(time)
t = 10-3 = 7 min.
It will take the customer 7 minutes to buy 5 coffees.
Feel free to ask for more if needed or if you did not understand something.
What is the value of y?
40°
Y + 30°
Answer:
y = 55
Step-by-step explanation:
The sum of the angles of a triangle are 180
40 + y+30 + y = 180
Combine like terms
70 +2y = 180
Subtract 70 from each side
2y = 180-70
2y = 110
Divide each side by 2
2y/2 = 110/2
y = 55
Sample Response: I agree that fast food
obsen gave work experience to teenagers. At
the same time, I wonder how valuable this
work experience is in Rise Red Nation,
Soloer mentions that teenagers with these
jobs are not paid well and often do not learn
new skills. In addition, time on the job can
take away from their focus on school.
What did you include in your response? Check all
that apply
an acknowledgement of the other
participant's opinion
my opinion on the topic
examples to support my opinion
evidence from a text related to the discussion
Answer:
you can pick any of them
Step-by-step explanation:
Answer: Any are right
Step-by-step explanation:
Which shows how to find the y-coordinate of the point that will divide CD into a 5:2 ratio using the formula y = (y2 – y1) + y1? y = (3 – 1) + 1 y = (3 + 4) – 4 y = (3 – 1) + 1 y = (3 + 4) – 4
Answer:
[tex]\frac{5}{5+2}(3-1)+ 1[/tex]
Step-by-step explanation:
To find the coordinate of the point that divides a line segment AB with point A at ([tex]x_1,y_1[/tex]) and point B at [tex](x_2,y_2)[/tex] in the proportion c:d, the formula used to find the location of the point is:
[tex]x-coordinate:\\\frac{c}{c+d}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{c}{c+d}(y_2-y_1)+y_1[/tex]
Therefore the y coordinate that divides line segment CD with point C at ([tex]-4,1[/tex]) and point D at [tex](3,3)[/tex] in the proportion 5:2 is given by:
[tex]for\ y-coordinate:\\\frac{c}{c+d}(y_2-y_1)+y_1\\=\frac{5}{5+2}(3-1)+ 1\\=\frac{5}{7}(2)+1=\frac{17}{7}[/tex]
Answer:
{5/7}(3-1)+1
Step-by-step explanation:
triangle ABC is Isosceles CA and CB are equal AB is parallels to the x- axis. Work out the coordinate of A. Given that BC=5cm work out the perimeter of the triangle
Answer:
The perimeter of the triangle ABC is 17 cm.
Step-by-step explanation:
Consider the Isosceles triangle ABC.
The sides CA and CB are equal with measures, 5 cm.
The base angles are assumed to be x° each. Hence, the angle ACB is 2x°.
The altitude CP divides the base AB into two equal halves and the angle ACB is also cut into halves.
Consider the right angled triangle ACP.
The sum of all the angles in a triangle is 180°.
Determine the value of x as follows:
x° + x° + 90° = 180°
2x° = 90°
x° = 45°
Compute the length of side AP as follows:
[tex]cos\ 45^{0}=\frac{AP}{CA}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{AP}{5}[/tex]
[tex]AP =\frac{5}{\sqrt{2}}\\\\AP=3.5[/tex]
Then the length of side AB is:
AB = AP + PB
= 3.5 + 3.5
= 7 cm
The perimeter of triangle ABC is:
Perimeter = AB + CA + CB
= 7 + 5 + 5
= 17
Thus, the perimeter of the triangle ABC is 17 cm.
f(x)=x^2. What is g(x)
Answer:
[tex]g(x) = \frac14x^2[/tex]
Step-by-step explanation:
Since f(x) and g(x) share the same top at (0,0), their difference is only a scale factor, so g(x) = ax² but we need to find a.
To find it, we use the given point of g, (2,1)
So g(2) = 1
meaning that
a·2² = 1
4a = 1
a = 1/4
the length f a rectangle is 3 ties its width, the perimeter of it is 24cm. what is the area of it?
Answer: 27cm²
Step-by-step explanation:
lets take the width as x and length as 3x( since length is 3 times the width)…
Perimeter of the rectangle is 24 cm( 2*(l+b))= 2×(3x+x):24
2×4x=24
8x=24
X( width): 24/8=3cm
Length= 3x: 3*3=9cm
Area of the rectangle: ( l*w)= 9×3: 27cm²
Answer:
Step-by-step explanation:
F(x)=x^2 what is g(x)
Given the function f(x) = −2x2 + 4x − 7, find f(−4).
−55
−7
9
25
Answer:
A. -55
Step-by-step explanation:
f(x)=-2x^2+4x-7
f(-4)= -2(-4)^2+4(-4)-7
= -2(16)-18-7
= -32-16-7
= -55
Answer:
-55
Step-by-step explanation:
f(x) = −2x^2 + 4x − 7
Let x = -4
f(-4) = −2(-4)^2 + 4(-4) − 7
= -2 (16) -16 -7
= -32 -16 -7
=-55
Line p and q are parallel lines. The slope of line q is-3. Determine the slope of line p. Type a numerical answer in the
space provided. If necessary, use the key to represent a fraction bar. Do not put spaces in your answer.
Answer:
The slope of p is also - 3 .
Since p and q are parallel their slope are also the same.
Hope this helps
Answer:
The slope of line p is also -3
Step-by-step explanation:
Recall that parallel lines have the property of carrying the exact same slope (that is why they don't intersect). Therefore if the slope of line q is -3, the slope of line p must also be -3.
3 cups a b c contain only salt and water the different mixtures are a salt:water 3:22 b Salt 1/8 c salt 12.75% what cup has the greatest proportion of salt
Answer:
Cup A
Step-by-step explanation:
Cup A
Salt: Water = 3:22
Expressed as a percentage
[tex]\dfrac{3}{22} \times 100 = 13.6\%[/tex]
Proportion of Salt =13.6%
Cup B
Salt: Water = 1:8
Expressed as a percentage
[tex]\dfrac{1}{8} \times 100 = 12.5\%[/tex]
Proportion of Salt =12.5%
Cup C
Proportion of Salt = 12.75%
Therefore, Cup A has the greatest proportion of salt.
Two consecutive odd whole numbers are selected. The difference between the reciprocal of the two numbers is 2/99. Determine the two numbers
Answer:
x = 9 (first odd number)
x + 2 = 11 (second odd number)
Step-by-step explanation:
Let
x =first odd number
x + 2=second odd number
given:
1/x - 1/(x + 2) = 2/99
Find the LCM
(x+2)-x / x(x+2)=2/99
x+2-x / x(x+2)=2/99
common denominator x( x + 2)
2 / x(x + 2) = 2/99
Take the reciprocal of both sides
1/2x(x + 2) = 99/2
multiply both by 2
x(x +2) = 99
Expand the left side
x^2 + 2x = 99
add 1 to both sides
x^2 + 2x + 1 = 100
express the left side as a square
(x + 1)^2 = 100
Square root of both sides
x + 1 = 10 or x + 1 = -10
taking the positive root only
x = 9 (first odd number)
x + 2 = 11 (second odd number)
check:
1/9 - 1/11 = 2/99
11/99 - 9/99 = 2/99
2/99 = 2/99
Find the value of x in the triangle shown below.
Answer:
It should be 50 degrees
Step-by-step explanation:
180-80= 100 degrees
making the two bottom angles combined angles equal to 100 degrees
100 divided by 2= 50 degrees making x=50 degrees
x= 50 degrees
Answer:
50°
Step-by-step explanation:
80+x+x=180
80+2x=180
2x=180-80
2x=100
100/2=50