What is the area of a triangle whose vertices are X(1, 1), Y(3, -1), and Z(4,4)?
Answer:
Step-by-step explanation:
Note that in this diagram, point A represents point X, point B represents point Y, and point C represents point Z.
From the diagram, it appears as if [tex]\overline{XZ} \perp \overline{XY}[/tex]. To determine if this is the case, we can find the slopes of both segments.
[tex]m_{\overline{XZ}}=\frac{4-1}{4-1}=1\\m_{\overline{XY}}=\frac{-1-1}{3-1}=-1[/tex]
Since these slopes are negative reciprocals, we know that they are perpendicular.
This means we can use the formula [tex]A=\frac{1}{2}bh[/tex], where b is the base (XY) and h is the height (XZ).
Note these are interchangeable.Using the distance formula,
[tex]XY=\sqrt{(3-1)^{2}+(-1-1)^{2}}=2\sqrt{2}\\XZ=\sqrt{(4-1)^{2}+(4-1)^{2}}=3\sqrt{2}[/tex]
This means the area is [tex]\frac{1}{2}(2\sqrt{2})(3\sqrt{2})=\boxed{6}[/tex]
Let p: The whole number has one digit.
Let q: The whole number is less than 10.
Which represents "The whole number has one digit if and only if the whole number is less than 10"?
pvq
p^q
p-q
p q
The whole number has one digit if and only if the whole number is less than 10.
Let p: The whole number has one digit.
Let q: The whole number is less than 10.
We have to determine the,
PVC
p^q
p-q
p q
What is a whole number?An integer is colloquially defined as a number that can be written without a fractional component.
The whole number has one digit if and only if the whole number is less than 10.
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The sample mean for the number of years worked is , and % of the employees in the sample worked for the company for at least 10 years. Round your answers to the nearest integer.
The sample mean for the number of years worked is 14, and 73% of the employees in the sample worked for the company for at least 10 years.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
The mean = (sum of service years) / employees in the sample worked
[tex](8+13+15+3+13+28+4+12+4+26+29+3+10+3+17+13+15+15+23+13+12+1+14+14+17+16+7+27+18+24) /30\\= (417 / 30)[/tex]
= 13.9 years
= 14 years
The percentage of employees who have worked for at least 10 years :
The number of employees with service years ≥ 10 years
= 22 employees
Total number of employees
Percentage (%) = (22 / 30)
= * 100%
= 0.7333 x 100%
= 73.33% = 73%
Therefore, The sample mean for the number of years worked is 14, and 73% of the employees in the sample worked for the company for at least 10 years.
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Find the 8th term of the arithmetic
sequence -2x -9,-7x - 2,
-12x + 5,...
Which of these correctly explains the solution of the system of equations shown below?
2 x + 3 y = 6
x + 3 y = 12
a) The values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution
b) The equations have y-intercepts at 2 and 4; therefore (2, 4) is the solution
c) The equations have x-intercepts at 3 and 12; therefore (3,12) is the solution
d) the lines representing the equations intersect at x = 1 and y = 0; therefore (1,0) is the solution
The values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)
Simultaneous linear equationFrom the question, we are to determine the solution of the given system of equations
The given system of equations are
2 x + 3 y = 6 ------- (1)
x + 3 y = 12 ------- (2)
From equation (2)
x + 3y = 12
Then, we can write that
x = 12 - 3y --------- (3)
Substitute this into equation (1)
2x + 3y = 6
2(12 -3y) + 3y = 6
24 - 6y + 3y = 6
24 -3y = 6
24 - 6 = 3y
18 = 3y
∴ y = 18/3
y = 6
Substitute the value of y into equation (3) to get the value of x
x = 12 - 3y
x = 12 -3(6)
x = 12 - 18
x = -6
∴ x= -6 and y = 6 ; Thus, (-6, 6) is a solution
Hence, the values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)
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Use ΔDEF, shown below, to answer the question that follows:
Triangle DEF where angle E is a right angle. DE measures x. DF measures 55. Angle F measures 49 degrees.
What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.
Answer: 41.51
Step-by-step explanation:
[tex]\sin 49^{\circ}=\frac{x}{55}\\x=55 \sin 49^{\circ} \approx \boxed{41.51}[/tex]
Which graph represents y = root(3, x) + 2 ?
Using translation concepts, the graph that represents [tex]y = \sqrt[3]{x} + 2[/tex] is given at the end of the question.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
[tex]y = \sqrt[3]{x} + 2[/tex] is a shift up of 2 units of [tex]y = \sqrt[3]{x}[/tex], hence the graph is given at the end of this question.
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On March 26, Samuel Griffin deposited $20,000 in a savings account that pays 5 5% interest compounded daily until July 24.
5 days in march.
31 days in May
30 days in June
24 days through July
rate of 5% each day.
so about 90 days of interest daily.
So 5% of 20,000
5 percent *20000
= (5/100)*20000
= (5*20000)/100
= 100000/100 = 1000
So 1,000 a day
1,000 * 90
= 90,000
A cylinder has a radius of 25 ft and a height of 14 ft. What is the surface area and volume of the cylinder?
3(x+4)=3(x)+3(4) distributive property
Answer:
3(x + 4) = 3(x) + 3(4)
3(x + 4) = 3x + 12
3x + 12 = 3x + 12
Subtract 12 from both sides
3x + 12 - 12 = 3x + 12 - 12
3x = 3x
3x - 3x = 3x - 3x
= 0
can you please help me? 2.1.1
Step-by-step explanation:
try this option (see the attachment), all the correct answers are marked with colour.
what is the value of the 9 in the number 2,448,901
When asking the value of '9' ⇒ in another number
⇒ means that it asking for the name of the position of that number in
the other number
Let's examine the name of the positions in the number:
⇒ look at the image attached
Based on the image:
⇒ 9 is the hundreds position of 2,448,901
Answer: hundreds
Hope that helps!
Answer:
Hundreds
Step-by-step explanation:
1=units
0=tens
9=hundreds
The average temperature at the South Pole is −45 F. The average temperature on the Equator is 92 F. Find the difference between the temperature at South Pole and at the Equator. Using simplified basic algebraic expressions
Answer:
-137
Step-by-step explanation:
The difference between two numbers can be found through subtraction.
-45 - 95 = -137.
Scientists are sending a rover to the moon. Their plan is to study a rectangular area of the moon by placing a grid over the map as shown. On the grid, 1 unit represents 1 kilometer (km).
the Rover will land at (3.5,1) , explore up to (3.5,4), and then over (2,4).
PART A. what are the coordinates of the fourth vertex of the rectangle that the scientist plan to explore ?
PART B.
what is a horizontal length of the rectangle? what is the vertical length of the rectangle
PART C. find the area of the Moon exploration area in square kilometers. Show your work.
The fourth vertex is (2, 1), and horizontal length is 1.5 km and the vertical length is 3 km. Then the area of the Moon exploration area will be 4.5 square km.
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L×W square units
Scientists are sending a rover to the moon.
Their plan is to study a rectangular area of the moon by placing a grid over the map as shown.
On the grid, 1 unit represents 1 kilometer (km).
PART A. Then the coordinates of the fourth vertex of the rectangle will be (2, 1).
PART B. Then the horizontal length of the rectangle will be 1.5 km and the vertical length of the rectangle will be 3 km.
PART C. Then the area of the Moon exploration area in square kilometers will be
Area = 3 x 1.5
Area = 4.5 square km
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Evaluate (-3 - y) / (x - 4) when x = -5 and y = -3
(-3 - y) / (x - 4)
(-3 - (-3)) / ((-5) - 4)
(0)/(-9)
0
hope it helps...!!!
Answer:
0
Step-by-step explanation:
[tex] \frac{ (- 3 - y)}{(x - 4)} \\ when \: x = - 5 \: \: y = - 3 \\ \frac{( - 3 - - 3)}{ (- 5 - 4)} = \frac{ - 3 + 3}{ - 9} \\ = \frac{0}{ - 9} \\ 0[/tex]
pls help asap i'll mark brainiest if its correct, 80 points.
Answer:
[tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]
Step-by-step explanation:
Given :
[tex]2\frac{1}{3} -\frac{1}{2} \div \frac{3}{4} + 3\frac{2}{3}[/tex]
=============================================================
Rewrite in improper fraction form :
[tex](\frac{6}{3} +\frac{1}{3}) -\frac{1}{2} \div \frac{3}{4} + (\frac{9}{3} +\frac{2}{3})[/tex]
[tex]\frac{7}{3} - \frac{1}{2} \div \frac{3}{4} + \frac{11}{3}[/tex]
=============================================================
Finding the common denominator :
⇒ 3 × 4
⇒ LCM = 12
============================================================
Solving with 12 as LCM :
⇒ [tex]\frac{7\times 4}{3 \times4} - \frac{1\times6}{2\times6} \div \frac{3\times3}{4\times3} + \frac{11\times4}{3\times4}[/tex]
⇒ [tex]\frac{28}{12} - \frac{6}{12} \div \frac{9}{12} + \frac{44}{12}[/tex]
⇒ [tex]\frac{28}{12} - \frac{2}{3} + \frac{44}{12}[/tex] [Division takes place first]
⇒ [tex]\frac{28}{12} - \frac{8}{12} + \frac{44}{12}[/tex]
⇒ [tex]\frac{28}{12} + \frac{36}{12}[/tex]
⇒ [tex]\frac{64}{12}[/tex]
⇒ [tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]
Which of the following functions best fits the data shown in the scatterplot below? y=100x+2 / y=20x^2+10 / y=4^x+8 / y=2^x+5
The equation of the scatter plot is (a) y = 100x + 2
How to determine the equation of the scatterplot?The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
The equation is then calculated as:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x - x_1) + y_1[/tex]
Substitute known values in the above equation
[tex]y = \frac{102 -2}{2-1}(x - 0) + 2[/tex]
Evaluate the expression on the right-hand side
y = 100x + 2
Hence, the equation of the scatter plot is (a) y = 100x + 2
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50 Points will mark Brainliest What is the circumference of circle P?
Express your answer in terms of π.
34π cm
68π cm
17π cm
58π cm
Answer:
[tex]34\pi[/tex] cm
Step-by-step explanation:
[tex]\text{A circle's circumference is equal to 2r, where PC is the radius.}[/tex]
[tex]\text{A circle's radius is the line traced from the circle's center to its perimeter.}[/tex]
[tex]\text{According to the figure, the radius is determined by the line drawn from the center}[/tex]
[tex]\text{P to the circumference C, which is PC, i.e. PC = radius = 17cm.}[/tex]
[tex]\text{We may get the circumference of a circle by substituting the radius value into the}[/tex]
[tex]\text{formula;}[/tex]
[tex]\text{2 (circumference) (17)}[/tex]
[tex]\text{Circumference =}[/tex] [tex]34\pi(\text{In terms of} \pi )[/tex]
Answer:
34π cm
Step-by-step explanation:
Hello!
The circumference of a circle is found using the formula [tex]P = 2\pi r[/tex]
r = radiusP = perimeterπ = piWe have the radius, PC(17), so we can plug it into the formula to find the perimeter.
Solve[tex]P = 2\pi r[/tex][tex]P = 2(17)\pi[/tex][tex]P = 34\pi[/tex]Since we are leaving it in terms of Pi, we don't have to further simplify it.
The perimeter is 34π cm.
-3+8x-5=-8 solve for x
The value of this equation is x = 0
The representation of an equation of the first degree - is given by:
[tex] \boxed{ \large \sf ax + b = 0}[/tex]
This representation is also defined in a first degree function.
— To solve this expression, let's: add or subtract the real terms. Then we will do the division.
⚘ Resolution
[tex] \large \sf{-3+8x-5=-8}[/tex]
[tex] \large \sf{-8+8x=-8}[/tex]
[tex] \large \sf{8x=0}[/tex]
[tex] \large \sf{x=0 \div 8}[/tex]
[tex] \green{ \boxed{ \boxed{ \blue{ \large \sf{x=0}}}}} \\ [/tex]
Therefore, the value of this equation will be x = 0
Wayne and Mack have
9 cats. Mack has twice
as many as Wayne.
How many cats does
Mack have?
Answer:
18
Step-by-step explanation:
mack has 18cats because she has 2×9 cats as Wayne 2×9 is 18
Answer:
18
Step-by-step explanation:
[tex]\sf Twice = *2\\9 * 2 = 18[/tex]
I need help with this answer please
Answer:
y=3x+1
Step-by-step explanation:
From the table when X=0,y=1 thus b=1.
When
solve this please and thank you
Answer:
-1/32
Step-by-step explanation:
1/4*1/8*1024 = 1024/32 = -32
Type your answer into the box.
Work out 0.58 million - 36,475
The difference between 0.58 million and 36,475 is 543,525 the answer is 543,525.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
= 0.58 million - 36,475
As we know,
1 million = 1,000,000
0.58 million = 580,000
= 580,000 - 36,475
= 543,525
Thus, the difference between 0.58 million and 36,475 is 543,525 the answer is 543,525.
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Determine the point(s), if any, at which the graph of the function has a tangent line with the given slope. Function y = x^2 + 2x Slope m = −8
The point at which the graph of the function has a tangent line with the given slope is (-5,15)
What is a tangent?A tangent is a straight line that touches any point on a curve.
Analysis:
slope of the curve [tex]x^{2}[/tex] + 2x is equal to dy/dx = d/dx( [tex]x^{2}[/tex] + 2x) = 2x+2
Which is equal to -8
2x+2 = -8
2x = -8-2
2x = -10
x = -5
substitute x into the equation
y = [tex](-5)^{2}[/tex] + 2(-5) = 25 - 10 = 15
In conclusion, the point at which the graph of the function has a tangent at -8 is (-5,15)
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Which shows the solution of the combined inequality?
−1≤2−j<−5
Number line ranging from negative six to zero with a line beginning with an open point at negative five and ending with a closed point at negative one
Number line ranging from negative six to zero with a line beginning with a closed point at negative five and ending with an open point at negative one
Number line ranging from zero to six with a line beginning with a closed point at one and ending with an open point at five
no solution
Step-by-step explanation:
if there is no typo, or there are no parts missing, then
-1 <= 2-j < -5
cannot have any solution, because already for the outside limits -1 < -5 is impossible. -1 is larger than -5 !
mohjjbn bn hjbjn hjbnm
(sin30°+cos30°)-(sin60°cos60°) find the value
write each equation in slope intercept form x+7y=48?
Answer:
[tex]y= -\dfrac 17 x +\dfrac{48}7[/tex]
Step-by-step explanation:
[tex]~~~~~~~x+7y = 48\\\\\implies 7y = 48-x\\\\\implies y = \dfrac 17(48-x)\\\\\implies y= -\dfrac 17 x +\dfrac{48}7\\\\\text{It now in the slope-intercept form (y = mx+c).}[/tex]
Find the value of: (3/4)^2 A. 9/16 B. 6/8 C. 6/4 D. 9/4
We are going to multiply the fraction 3/4, to the power of 2.
This means that:
3 will be multiplied 2 times.4 will multiply 2 timesTherefore:
[tex]\bf{\left(\dfrac{3}{4}\right)^{2}=\dfrac{3\times3}{4\times4}=\dfrac{9}{16} }[/tex]
Therefore, the answer of the fraction (3/4)^2, is equal to 9/16.
The correct option is "A".[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
7. Look at the number sentence below.
1+2+3+4 +-----------+ 80 = 3240
71 +72+73+ ---------+ 80 = 755
What is the sum of numbers from 1 to 70?
a)3240-10
b) 3240-80
c) 3240 +755
d) 3240-755
Answer: 3240-755
Step-by-step explanation:
We know that:
[tex](1+2+\cdots+80)-(71+72+\cdots+80)=1+2+\cdots+70[/tex]
Thus, [tex]1+2+\cdots+70=\boxed{3240-755}[/tex]