Answer:
1) y > x
2) x > 5 > y
3) x ≤ 4 ( or 4 ≥ x )
4) x = y
Step-by-step explanation:
1) 1. y is greater than x
2. so y > x
2) 1. 5 is less than x and more than y
2. we can write this like x > 5 > y
3. you can just squish them together as a shortcut usually: x > 5 and 5 > y --> x > 5 > y
3) 1. x is for at most, we can say this as x is less than or equal to 4
2. this is written as x ≤ 4 or 4 ≥ x
4) 1. x - y = 0 so x and y must be the same value
2. therefore x = y
Consider in the figure below.
The perpendicular bisectors of its sides are , , and . They meet at a single point .
(In other words, is the circumcenter of .)
Suppose , , and .
Find , , and .
Note that the figure is not drawn to scale.
Here BD is perpendicular bisector
So
UB=BV=74[tex]\\ \tt\hookrightarrow UV=74+74=148[/tex]
Apply Pythagorean theorem
[tex]\\ \tt\hookrightarrow BD^2=UD^2-UB^2=UD^2-VD^2[/tex]
UD=VD=78=TD[tex]\\ \tt\hookrightarrow TC^2=TD^2-CD^2[/tex]
[tex]\\ \tt\hookrightarrow TC^2=78^2-30^2[/tex]
[tex]\\ \tt\hookrightarrow TC^2=6084-900=5184[/tex]
[tex]\\ \tt\hookrightarrow TC=72[/tex]
Answer:
UV = 148
VD = 78
TC = 72
Step-by-step explanation:
BD is the perpendicular bisector of side UV.
Therefore, ΔUDV is an isosceles triangle.
This implies that UD = VD and BV = UB so UV = 2 x BV
Given that UD = 78, and UD = VD, then VD = 78Given that BV = 74, and BV = UB, then UV = 2 x 74 = 148ΔUDC is a right triangle.
Given CD = 30 and UD = 78,
and using Pythagoras' Theorem, we can calculate UC:
UC = √(UD² - CD²)
⇒ UC = √(78² - 30²)
⇒ UC = 72
CD is the perpendicular bisector of side UT.
Therefore, ΔUDT is an isosceles triangle, so UC = TC
Since UC = 72, then TC = 72
Please help its very hard
Answer:
16 dollars
Step-by-step explanation:
The price includes the price of an empty bag B and the price of popcorn that is proportional to x (the number of ounces). Let each popcorn cost A$. Then the price of bag y = Ax + B
Given x = 10, y = 6, so 6 = 10A + B (1)
Given x = 20, y = 8, so 8 = 20x + B (2)
(2) - (1): 2 = 10A, so A = 2/10 = 0.2
Sub it into (1), 6 = 10*0.2 + B = 2 + B, so B = 6 - 2 = 4
We got y = 0.2x + 4
Check: x = 35, y = 0.2*35 + 4 = 11 (right)
x = 48, y = 0.2*48 + 4 = 13.6 (right)
Now find y when x = 60
y = 0.2*60 + 4 = 16 dollars
HELP Solve the system of equations using the substitution method.
-7x - 4y = -11
y = x
Answer:
y = - 7/4 x + 1 1 / 4
Step-by-step explanation:
Find the Value of y when y=3x+45 and x=7
102
15
35
66
Answer:
y = 66
Step-by-step explanation:
y=3x+45
putting the value of x in equation which is 7 .
=> y = 3(7)+45
=> y = 21+45
=> y = 66
There is exactly
1 pair of parallel sides in the following shape.
What is the area of the shape?
The given properties of one pair of parallel sides in the four sided
quadrilateral, indicates that the shape is a trapezium.
Response:
The area of the shape is 35 square unit How can the area of the given quadrilateral be calculated?Given that the side with length 6 is parallel to the side with length 8, we
and that the figure is four sided, we have;
The given figure is a trapezium;
[tex]Area \ of \ a \ trapezium = \mathbf{ \dfrac{a + b }{2} \times h}[/tex]Where;
a and b = The lengths of the parallel sides
h = The height of the figure = 5
Which gives;
[tex]Area = \dfrac{6 + 8 }{2} \times 5 = \mathbf{35}[/tex]
The area of the shape = 35 square unitLearn more about trapeziums here:
https://brainly.com/question/96136
Answer:35 sq units
Step-by-step explanation:
simple ! please show work math experts :) thank you and have a wonderful day
Answer:
1) [tex]\dfrac78[/tex]
2) [tex]\dfrac{17}{12} = 1 \frac{5}{12}[/tex]
3) [tex]\dfrac{53}{12}=4 \frac{5}{12}[/tex]
Step-by-step explanation:
1)
[tex]\dfrac38+\dfrac12=\dfrac38+\dfrac{1 \times4}{2 \times 4}=\dfrac38+\dfrac48=\dfrac78[/tex]
2)
[tex]\dfrac23+\dfrac34=\dfrac{2 \times 4}{3 \times 4}+\dfrac{3 \times3}{4 \times3}=\dfrac8{12}+\dfrac{9}{12}=\dfrac{17}{12}=1 \frac{5}{12}[/tex]
3)
First convert mixed number into improper fraction:
[tex]4 \frac23=\dfrac{3\times4+2}{3}=\dfrac{14}{3}[/tex]
[tex]\implies 4 \frac23-\dfrac{3}{12}=\dfrac{14}{3}-\dfrac{3}{12}=\dfrac{14\times4}{3\times4}-\dfrac{3}{12}=\dfrac{56}{12}-\dfrac{3}{12}=\dfrac{53}{12}=4 \frac{5}{12}[/tex]
Seven times the product of negative six and a number
Hi!
I can help you with joy! :)
7 times the product of -6 and a number. Let the number be
a. Now, "the product of" means we multiply.
Multiply -6 times a: -6a
If you notice, we write the number before the variable.
Now, multiply 7 times -6a:
7(-6a)
Simplify:
-42a
I hope this helps!
Have a Great Day!
-Content Girl
[tex]\bf{Mysterious^a^n^d\:M^a^gi^ca^l[/tex]
The pair of values below is from an inverse variation. Find the missing value.
(4,17). (8,y)
Answer:
8.5
Step-by-step explanation:
For inverse variation of (x, y), x*y = constant
so 4*17 = 8*y
y = 4*17/8 = 17/2 = 8.5
help plsssssssssssssss
Answer:
63x + 18
Step-by-step explanation:
9 multiply 7x to give 63x
and 9 multiplies 2 to give 18
Answer:
Option C. 63x +18 is correct.
Step-by-step explanation:
7x ×9= 63x
2×9=18
=63x + 18
Hope it helps.......
Given the points (9,9) and (-6, -10) find the slope.
m =
1. Observe question
2. Employ Point-Slope formula
(y2 - y1)/(x2 - x1 )=
(-10-9)/(-6-9) =
-19/-15=
19/15
Slope: 19/15
Answer:[tex]\frac{19}{15}[/tex] or 1.26667
Step-by-step explanation:
m=rise over run=Δy over Δx
m=y2−y1x2−x1
m=−10−9−6−9
m=−19−15
m=19/15
Which values are greater than -2?
-5 -4 -3 -2 -1 0 1 2 3 4 5
WILL MARK BRAINLIEST
Answer:
-1, 0, 1, 2, 3, 4, 5 are the values greater than -2
Step-by-step explanation:
Let's imagine a number line.
Numbers that are bigger are on the right side of the number line.
The numbers to the right of -2 are:
-1 one greater0 two greater1 three greater2 +43 +5 4 +65 +7And so on...
Numbers that would be less than -2 will be on the left side
-3 1 less-4 2 lessetc...
-Chetan K
Answer:
-1,0,1,2,3,4,5
ep-by-step explanation:
think of it on a number line
If (-3, y) lies on the graph of y = (1/2)^x, then y =
-8
8
1/8
Un aventurero realiza 2/5 de un viaje en todo terreno,1/3 a caballo y el resto andando. Si la caminata ha sido de 80 km, ¿cuál es la longitud total de su recorrido?
Answer:
Todo terreno+ caballo+caminado=distancia ; (2/5)d+(1/3)d+80=d
Step-by-step explanation:
Pierre is waiting to be seated at a popular restaurant where the waiting time is a random variable with an exponential PDF, and the mean waiting time is 75 minutes. Pierre has already been waiting for 40 minutes. What is the probability that Pierre will have to wait more than 30 more minutes, given that he has already waited 40 minutes? Compute your answer rounded to 4 decimal places.
The PDF for the wait time (denoted by the random variable X) is
[tex]f_X(x) = \begin{cases}\lambda e^{-\lambda x} & \text{if }x \ge 0 \\ 0 &\text{otherwise}\end{cases}[/tex]
where λ = 1/75. We want to find Pr[X > 70 | X ≥ 40]. Pierre has already been waiting for 40 min, so if he waits another 30 min he will have waited for a total of 70 min.
By definition of conditional probability,
Pr[X > 70 | X ≥ 40] = Pr[X > 70 and X ≥ 40] / Pr[X ≥ 40]
If X > 70, then automatically X ≥ 40 is satisified, so the right side reduces to
Pr[X > 70 | X ≥ 40] = Pr[X > 70] / Pr[X ≥ 40]
Use the PDF or CDF to find the remaining probabilities. For instance, using the PDF,
[tex]\mathrm{Pr}[X > 70] = \displaystyle \int_{-\infty}^{70} f_X(x) \, dx = \int_0^{70} f_X(x) \, dx \approx 0.3932[/tex]
Or, using the CDF,
[tex]F_X(x) = \displaystyle \int_{-\infty}^x f_X(t) \, dt = \begin{cases}0&\text{if }x<0 \\ 1-e^{-\lambda x} & \text{if }x \ge 0\end{cases}[/tex]
[tex]\implies \mathrm{Pr}[X > 70] = 1 - \mathrm{Pr}[X \le 70] = 1 - F_X(70) \approx 0.3932[/tex]
Similarly, you'll find that Pr[X ≥ 40] ≈ 0.5866.
It follows that
Pr[X > 70 | X ≥ 40] ≈ 0.3932 / 0.5866 ≈ 0.6703
Let f be the function given by f(x)=3ln(2+x2)cosx. What is the average value of f on the closed interval 2≤x≤6?
The average value of f(x) over [2, 6] is given by the definite integral,
[tex]\displaystyle f_{\rm ave[2,6]} = \frac1{6-2} \int_2^6 3\ln(2+x^3)\cos(x) \, dx[/tex]
and is approximately -1.67284.
The approximate average value of the function in the closed interval [2,6] is -1.628.
It is given that the f is the function given by: [tex]\rm f(x) = 3ln(2+x^2)cosx[/tex]
It is required to find the average value of f in the closed interval [2,6]
What is integration?It is defined as the mathematical approach to calculating the smaller parts or components.
We have function f:
[tex]\rm f(x) = 3ln(2+x^2)cosx[/tex]
For the average value in [2,6]
We integrate the function with lower limit 2 and higher limit 6.
[tex]\rm \int_{2}^{6}f(x) =\int_{2}^{6}( 3ln(2+x^2)cosx)\\[/tex]
The average value of the above function:
[tex]\rm =\frac{1}{6-2} \int_{2}^{6}( 3ln(2+x^2)cosx)\\[/tex]
Further solving:
[tex]\rm =\frac{3}{4} \int_{2}^{6}( ln(2+x^2)cosx)\\[/tex]
Further solving and applying limits we get:
[tex]=\frac{3}{4}\times-2.2304[/tex]
= -1.628
Thus, the approximate value of the function in the closed interval [2,6]
is -1.628.
Learn more about the integration here:
https://brainly.com/question/14502499
Number 3
Number 2 is done but part of it
Answer:
I believe the answer is B.1
Find slope: PLEASE HELP !
Take 2 points
(-7,4)(2,6)Slope:-
[tex]\\ \rm\hookrightarrow m=\dfrac{6-4}{2+7}[/tex]
[tex]\\ \rm\hookrightarrow m=\dfrac{2}{9}[/tex]
[tex]\\ \rm\hookrightarrow m=0.2[/tex]
What is the volume and surface area of a rectangular prism that is 11 ft long, 8 ft wide, and 4 ft tall?
Select all the correct answers.
V = 352 f1
V = 152 ft
V - 23 ft
SA = 480 ft
SA = 328 ft
SA = 92 ft
Answer:
The volume of the rectangular prism is 352 ft. The total surface area is 328 ft.
Step-by-step explanation:
Volume:
V = whl
V = 8 x 4 x 11
V = 352 ft
For finding surface area you have to find the lateral surface area: 152 ft, top surface area: 88 ft, and the bottom surface area: 88 ft. Add all that up and you get 328 ft.
Use the given information to prove the following theorem.
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
We let be any point on line , but different from point .
Let's proof
PQ is the perpendicular bisector Hence
CQ=DQ(Bisected sides)Now apply Pythagorean theorem
[tex]\\ \tt\hookrightarrow PQ^2+QD^2=PD^2[/tex]--(1)
[tex]\\ \tt\hookrightarrow PQ^2+CQ^2=PC^2[/tex]
As QD=CD
[tex]\\ \tt\hookrightarrow PQ^2+QD^2=PC^2[/tex]--(2)
From (1) and (2)
[tex]\\ \tt\hookrightarrow PC^2=PD^2[/tex]
[tex]\\ \tt\hookrightarrow PC=PD[/tex]
Answer:
Given [tex]\overline{\rm PQ}[/tex] is the [tex]\perp[/tex] bisector of [tex]\overline{\rm CD}[/tex]
⇒ [tex]\overline{\rm CQ}=\overline{\rm CD}[/tex]
⇒ ΔPQD ≅ ΔPQC
⇒ CP = PD
Step-by-step explanation:
Given [tex]\overline{\rm PQ}[/tex] is the [tex]\perp[/tex] bisector of [tex]\overline{\rm CD}[/tex]
⇒ [tex]\overline{\rm CQ}=\overline{\rm CD}[/tex]
⇒ ΔPQD ≅ ΔPQC
⇒ CP = PD
Write the ratio of the first measurement to the second measurement Compare in inches. 3 feet to 31 inches. type the ratio as a simplified fraction.
Will give 50points Pleasee help urgent!
Answer:
a = 10; a = 2
Step-by-step explanation:
Step 1: Use the Pythagorean theorem to solve this equation
1. Orignal eqaution: (a + 2)² + (a - 5)² = (a + 3)²
2. Expand (a + 2)² + (a - 5)² which will give us 2a² - 6a + 29
3. Expand (a + 3)² giving us a² + 6a + 9
4. Simplified equation: 2a² - 6a + 29 = a² + 6a + 9
Step 2: Subtract 9 from both sides
1. 2a² - 6a + 29 - 9 = a² + 6a + 9 - 9
2. Simplify: 2a² - 6a + 20 = a² + 6a
Step 3: Subtract 6a from both sides
1. 2a² - 6a + 20 - 6a = a² + 6a - 6a
2. Simplify: 2a² -12a + 20 = a²
Step 4: Subtract a2 from both sides
1. 2a² - 12a + 20 - a² = a² - a²
2. Simplify: a² - 12a + 20 = 0
Step 5: Use the quadratic formula to solve for a
1. Quadratic formula: a = -b += √b² - 4ac/2a
2. Plug in the correct values: a = -(-12) += √(-12)² + 4(1)(20)/2(1)
3. Simplify the numerator and denominator: 12 += 8/2
4. Final equation: a = 12 - 8/2 or a = 12 + 8/2
5. Hence, the answer is 10 or 2
What is the area of the drawing of the trophy shown?
Answer:
The area of the drawing is 12 Squares
For the functions f(x) = x+2 and g(x) = x^2 - 3 which expression has the greatest value?
A. f(g(1))
B. f(g(-2))
C. g(f(-4))
D. g(f(-2))
2. Find g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3
A. 9
B.8
C.329
D.536
The expression which has the greatest value is; Choice B: f(g(-2))
The value of g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3 is; 586
The value of functionsQuestion 1;
From the information given;
g(f(x)) = x²+4x +1f(g(x)) = x² -1.Hence, from the options given; upon substitution, it follows that the expression with the greatest value is;
f(g(-2)) = (-2)² -1 = 4-1 = 3.Question 2;
From the task content;
g(f(x)) = 64x² + 140x + 122Hence, upon substitution of -4 into the function;
g(f(-4)) = 64(-4)² + 140(-4) + 122g(f(-4)) = 586Read more on functions of functions;
https://brainly.com/question/4528336
10. Triangle ABC is formed by two parallel lines and two other intersecting
lines. Find the measure of each angle A, B, and of the triangle.
61°
47
с
47
Answer:
A:61°
B:72°
C:47°
Explanation:
I took the test and it was correct
Divide.
2x4 + 11x3 + 13x2 + 2x - 8 = x +4
Answer:
x=-55
Step-by-step explanation:
(2)(4)+(11)(3)+(13)(2)+2x−8=x+4
Simplify both sides of the equation.
8+33+26+2x+−8=x+4
Combine like terms
(2x)+(8+33+26+−8)=x+4
2x+59=x+4
2x+59=x+4
Subtract from both sides
2x+59−x=x+4−x
x+59=4
Subtract 59 from both sides
x+59−59=4−59
x=−55
write your own situation in which speed, s, is an independent variable.
Answer:
We want to use time so we will say
The time it takes to finish a jog, t, at the speed of s.
Step-by-step explanation:
The dependent variable we know depends on the independent variable.
Our independent variable is speed because it represents itself where time depends on speed. The reason it depends on speed is that the time to finish a jog depends on your speed.
1. A. What is the mean absolute deviation of the following data set? Round to the nearest hundredth if necessary.
p.s. I need the work on how to find it
Help me please please please
Answer:
GPA ≈ 2.67
Step-by-step explanation:
Grade points are weighted by credit hours:
GPA = ∑(grade points×credit hours) / ∑(credit hours)
GPA = (3×2 +2×4 +4×3 +2×3)/(2 +4 +3 +3)
= (6 +8 +12 +6)/12 = 32/12 = 2 2/3
GPA ≈ 2.67
What is the slope of the line that passes through the points (-2,9) and (8,34)?
Write your answer in simplest form.
Answer:
2.5
Step-by-step explanation:
y=ax+b
9= -2a+b <=> b= 9+2a
34=8a+b = 8a+9+2a = 10a + 9
a = (34-9)/10 = 2.5
Answer:
m = 2.5Step-by-step explanation:
Use the slope formula:
m = (y₂ - y₁)/(x₂ - x₁)m = (34 - 9)/(8 - (-2)) = 25/10 = 2.5Graph the equation y=1/2x
Answer/Step-by-step explanation:
The graph of the equation y = 1/2x on the coordinate plane is plotted below
The given equation is:
y = 1/2x
The equation is of the form:
y = mx + c
where m represents the slope
and c represents the y-intercept
Comparing the equation y = 1/2x with y = mx + c
The slope, m = 1/2
The y-intercept, c = 0
The line graph with slope, m = 1/2, and y-intercept, c = 0 is plotted below
[RevyBreeze]