Answer:
∠PQT = 97°
∠SQR = 83°
Step-by-step explanation:
Supplementary angles sum to 180°
⇒ ∠PQT + ∠SQR = 180°
Given:
∠PQT = (3x + 43)°∠SQR = (6x - 25)°Therefore:
⇒ (3x + 43) + (6x - 25) = 180
⇒ 3x + 6x + 43 - 25 = 180
⇒ 9x + 18 = 180
⇒ 9x = 162
⇒ x = 18
Substitute the found value of x into the expression for each angle:
⇒ ∠PQT = (3x + 43)°
⇒ ∠PQT = (3(18) + 43)°
⇒ ∠PQT = 97°
⇒ ∠SQR = (6x - 25)°
⇒ ∠SQR = (6(18) - 25)°
⇒ ∠SQR = 83°
Check
⇒ ∠PQT + ∠SQR = 97° + 83° = 180°
what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96
Answer:
A. 24
Step-by-step explanation:
Least common multiple of 8 and 12 = 24
8× 1 = 8 12×1 = 12
8×2 = 16 12×2=24
8×3 = 24
L.C.M (8,12) = 24
The greatest multiple that occurs in both the multiples of 8 and 12, is 24.
Hence, the least common multiple here is 24.
what is next number in pattern 7, 11, 2, 18, -7
Answer:
the answer is -7+-25=-32
Let −5, 3 be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.
The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have (−5, 3) be a point on the terminal side of θ.
Perpendicular = -5
Base = 3
From Pythagoras' theorem:
Hypotenuse² = (3)² + (-5)²
Hypotenuse = √34
cosθ = 3/√34
cscθ = -√34/5
tanθ = -5/3
Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
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An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?
$450
$400
$550
None of these choices are correct.
Answer:
$800
Step-by-step explanation:
per hour $40×10hours=$400
$400÷$50=8 times initial fee
8×$50=$400 total initial fee
$400hours fee+$400 initial fee=$800 total payment
NEED HELP ASAP !!!
Simplify: √16r
O 47²
O 473
87²
O 8-3
Answer:
4 r^3
Step-by-step explanation:
sqrt ( 16 r^6 ) = sqrt ( 4^2 * (r^3)^2 ) = 4 r^3
Let f(t) represent the temperature of a turkey baking in an oven as a function of time (t) in the oven (in minutes). This means time (t) is the independent variable and temperature of the turkey f(t) is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an oven, the temperature of the oven stays constant. The graph of the function is shown below.
Describe the rate of change pattern over each interval of the graph listed below.
a. 0 < t < 345
b. 345 < t < 360
c. t > 360
Explain what is happening in each interval of your graph in terms of the turkey and its temperature, using complete sentences.
Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation.
Answer:
a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.
b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.
c. When the time is greater than 360 minutes, the temperature of the turkey decreases.
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard
Which formula finds the probability that a point on the grid below will be in the blue area? A grid contains 20 squares. 10 squares are shaded blue. P (blue) = StartFraction total number of squares over number of blue squares EndFraction P (blue) = StartFraction number of blue squares over total number of squares EndFraction P (blue) = StartFraction number of blue squares over number of white squares EndFraction P (blue) = StartFraction number of white squares over number of blue squared EndFraction
The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:
P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.
The probability = 1/2.
The probability of an event defines the chance of the occurrence of that event. It is given by the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.
If we suppose an event to be A, the total number of possible outcomes favorable to A be n, and the total number of outcomes in the experiment be S, then the probability of event A can be given as:
P(A) = n/S.
In the question, we are asked to find the formula that defines the probability that a point on the grid will be in the blue area, where the grid contains 20 squares, 10 of them being shaded blue.
We take the event that the chosen point is in the blue area as A.
The total number of outcomes favorable to this event A can be given by n, which will be equal to the number of blue squares = 10
The total number of outcomes in the experiment can be given by S, which will be equal to the number of squares = 20.
Now, the formula for the probability of event A can be written as
P(A) = n/S = 10/20 = 1/2.
The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:
P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.
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A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Answer:
1/(7^5)=1/16807
Step-by-step explanation:
Assuming 7-key mean zero up to 7,
# of possible codes = 17^5 = 16807
=====
Probability of first try correct = 1/7^5
If f(x) =
√2x+3
6x-5
a. 1
b. -2
then f() =
C. -1
d. - 13
Answer:
put 1/2as a value of x in the equation and then solve .then the answer will be -1
Answer:
[tex]C.\ f\left( \frac{1}{2} \right) =-1[/tex]
Step-by-step explanation:
[tex]f\left( x\right) =\frac{\sqrt{2x+3} }{6x-5}[/tex]
In order to calculate f(1/2) ,all we have to do
is replacing x by 1/2 in the expression of f.
Then
[tex]f\left( \frac{1}{2} \right) =\frac{\sqrt{2\left( \frac{1}{2} \right) +3} }{6\left( \frac{1}{2} \right) -5 }[/tex]
[tex]=\frac{\sqrt{1+3} }{3-5}[/tex]
[tex]=\frac{\sqrt{4} }{-2}[/tex]
[tex]=\frac{2}{-2}[/tex]
[tex]=-1[/tex]
2.
Julia grows flowers in a garden that is the shape of a rectangle. The side lengths of
the garden are shown in the diagram.
5½⁄2 feet
3 feet
Which of these is equal to the area of the garden? Select all that apply.
A. 8
square feet
1
B.
5
feet x 3 feet
2
C.
151/11
square feet
D. 16
16¹ square feet
E. 5 feet +
11/12
F. (5 feet x 3 feet) +
foot + 3 feet
for
foot
The area of the rectangular garden given the length and width is 16 1/2 square feet
Area of the gardenLength = 5 1/2 feetWidth = 3 feetArea of a rectangular garden = length × width
= 5 1/2 feet × 3 feet
= 11/2 × 3
= 33/2
= 16 1/2 square feet
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A company had the following purchases and sales during its first year of operations:
Purchases Sales
January: 10 units at $120 6 units
February: 20 units at $125 5 units
May: 15 units at $130 9 units
September: 12 units at $135 8 units
November: 10 units at $140 13 units
The final answer of the Inventory is $3540.
What is Inventory?The term inventory refers to the raw materials used in production as well as the goods produced that are available for sale.
FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold
Ending inventory comprises of goods bought in May, September and November
cost of the ending inventory :
(4 x $130) + (12 x $135) + (10 x$140) = $3540
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5 ice creams cost 6.50 pounds. How much do 11 ice creams cost
Answer:
14.30
Step-by-step explanation:
6.50/5=1.3
so one ice cream is 1.30 pounds
1.30X11=14.3
so 11 ice creams is 14.30 pounds
Christine splits 4/5 pounds of candy with 5 people. What is the unit rate in pounds per person. In simplest form
Answer:
4/25
Step-by-step explanation:
4/5 ÷ 5 = 4/5 × 1/5 = 4/25
Can you please help meee
Answer: y = 4x + 5/4
Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.
Answer this! Thanks so much in advance (:
Answer:
ai) m = 17, applicable past x = 23/17; aii) m = 4; applicable past 3 dad jokes
Step-by-step explanation:
to calculate slope you use the (y2 - y1) / (x2 - x1) equation
so for the first one
(62 - 11) / (5 - 2)
51 / 3 = 17
the equation for this is y = 17x + b
plug in values to find b
11 = 34 + b
b is -23
y = 17x - 23
because distance cannot be negative we must find when x is exactly 0 to find where it is applicable
17x = 23
x = 23/17
for the second one we can subtract again
(10 - 2) / (5 - 3)
8 / 2
4 is the slope
like before we must find b and then find where y is 0
y = 4x + b
2 = 12 + b
b = -10
y = 4x - 10
4x = 10
x = 5/2
since you cannot have 1/2 a dad joke we round up from 2 1/2 to 3
HELP pls. Which statement correctly demonstrates using limits to determine a vertical asymptote of
Answer:
Step-by-step explanation:
what is the sign of f on the interval -5/9 < X < 2/3
Note that the sign of f on the interval -5/9 < x < 2/3 is negative. (Option B)
What is the explanation for the above?To determine the sign of f(x) on the interval -5/9 < x < 2/3, we need to evaluate f(x) at a test point within this interval and determine if it is positive or negative.
Since we know that f(x) has zeros at x = -4, x = -5/9, and x = 2/3, we can use these points as our reference to choose test points.
Specifically, since the zeros at x = -5/9 and x = 2/3 are not included in the interval -5/9 < x < 2/3, we can choose any test point within this interval, such as x = 0.
Evaluating f(x) at x = 0, we get:
f(0) = (3(0) - 2)(0 + 4)(9(0) + 5)
= (-2)(4)(5)
= -40
Since f(0) is negative, we can conclude that f(x) is negative on the interval -5/9 < x < 2/3.
Therefore, the sign of f on the interval -5/9 < x < 2/3 is negative
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Full Question:
f(x) = (3x - 2) (x+4) (9x +5) has zeros at x = -4, x = -5/9, and x = 2/3, that is the sign of f on the interval -5/9 < x < 2/3?
Translate and solve using proportions what percent of 120 is15
Answer:
12.5%
Step-by-step explanation:
To find what percent of 120 15 is, we must find what 15/120 is.
15/120 = 0.125. To convert to a percent, we move the decimal two places to the right. So, the answer is 12.5%.
Brainliest, please :)
Answer:
12.5%
Step-by-step explanation:
Please answer both questions I will give u brainliest if ur right
first one b 315, second d
Step-by-step explanation:
18*=3*+315
7*+4*=a*
A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The difference is only 0.04, but that is still a significant change.
The margin of error is quite small compared to the change year over year, so it is a significant issue.
The change of 0.09 is not a lot and thus should be ignored.
The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.
The correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
We have:
A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C.
As the value of MOE is 0.13 degrees
It is a serious problem because the margin of error is quite narrow in comparison to the shift from year to year.
Thus, the correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.
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pls someone help me asap :)
Answer:
right angle
acute
acute
obtuse
obtuse
Step-by-step explanation:
Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.
< DBF = <DBE + <EBF
< DBF = 25 + 65 = 90 (right angle)
<EBD = 25 (given) (acute)
<DBC = 50 (given) (acute)
<ABE = <ABF + <FBE
<ABE = 40 + 65
<ABE = 105 (obtuse)
<CBF = <CBD + <DBE + <EBF
<CBF = 50 + 25 + 65
<CBF = 140 (obtuse)
There are 10 USB drives in a box and 3 are defective. Two drives are to be selected, one after the other. What is the probability of selecting a defective USB followed by another defective USB?
[tex]|\Omega|=10\cdot9=90\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6.7\%[/tex]
Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.
Which is the equation for y?
Answer:
y = -t
Step-by-step explanation:
Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
⇒ parametric equation of line passing through a point (a₁, b₁, c₁)
and parallel to a vector <a, b, c> is given by :
x =a₁ + at , y = b₁ + bt , z = c₁ + ct
now according to question:
given -
point, P(1, 0, -3)
line, x = −1 + 2t , y = 2−t, and z = 3+3t.
so from the line the vector is= <2, -1, 3>
now using above formula,
equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.
we have to solve for 'y' only,
⇒ y = -t (answer)
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Which graph represents the function
there are 2 more graphs but it won't add it
Answer:
[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]
so y = 3x - 3
since 3x + 6 is on the bottom,
[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]
so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)
pls help oooooooooooo
Answer:
110
Step-by-step explanation:
Suppose lines EH and BD are parallel:
Angle <GFE and angle <ABC are supplementary so their sum is equal to 180
2x + 10 + x + 20 = 180 add like terms
3x + 30 = 180 subtract 30 from both sides
3x = 150 divide both sides by 3
x = 50
We are asked the value of <ACD
<ABD and <ACD are also supplementary so we can find the value od <ACD:
x + 20 + <ACD = 180 we know x = 50 so we can replace x with that
50 + 20 + <ACD = 180
70 + <ACD = 180 subtract 79 from both sides
<ACD = 110
find sin(x/2), cos (x/2), and tan(x/2) from the given information.
Sin(x)= 15/17, 0 < x <90
sin(x/2)= ?
cos(x/2)=?
tan(x/2)= 0.6
I need help with sin and cos. I know what tan is.
Step-by-step explanation:
sin(x/2) = sqrt((1 - cos(x))/2)
cos(x/2) = sqrt((1 + cos(x))/2)
tan(x/2) = sin(x/2)/cos(x/2)
sin(x) = 15/17
so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.
via Pythagoras we get the 3rd, horizontal side :
17² = 15² + side²
289 = 225 + side²
64 = side²
side = 8
cos(x) = 8/17
sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =
= 0.514495755...
cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =
= 0.857492926...
tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =
= 3/5 = 0.6
f(x)= 2x^3 + 6x^2 -5x - 3, g(x)= 3x-4 find (f-g)(x)
The difference in the given functions is 2x^3 + 6x^2 -8x + 1
Difference of functionsGiven the following function a shown
f(x)= 2x^3 + 6x^2 -5x - 3
g(x)= 3x-4
Take the difference
(f-g)(x) = f(x) - g(x)
Substitute
(f-g)(x) = 2x^3 + 6x^2 -5x - 3 - (3x - 4)
Expand
(f-g)(x) = 2x^3 + 6x^2 -5x - 3 - 3x + 4
(f-g)(x) = 2x^3 + 6x^2 -8x + 1
Hence the difference in the given functions is 2x^3 + 6x^2 -8x + 1
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Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
40 divided by (negative 10)
40 divided by 10
40 divided by 40
40 divided by 40
Answer:
40 divided by 10
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
urgent algebra 2 help please
Answer:
y = 4x - 5
Step-by-step explanation:
y = mx + b
By putting above values in equation (i)
-1 = 4 (1) + b
-1 = 4 + b
-5 = b
b = -5
y = 4x - 5
