Answer:
???
Step-by-step explanation:
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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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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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]
When you are trying to find the mean in a dot plot do you want to use the number of dots of the actual number underneath of the dots?
The number of dots tells us how many times we need to add the actual number underneath the dots. So you need to use both.
Which number should you use for the mean?
Let's suppose we have the next set:
{2, 2, 2, 4, 5, 5, 6}
If you graphed it in a dot plot, then you will have:
3 dots above the number 2.1 dot above the number 4.2 dots above the number 5.1 dot above the number 6.A total of 7 dots.
To find the mean, we just compute:
[tex]M = \frac{2 + 2 + 2 + 4 + 5 + 5 + 6}{7} = 3.7[/tex]
So the number of dots tells us how many times we need to add the actual number underneath the dots. In conclusion, to find the mean you need to use both, the number of dots and the number underneath.
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-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]
A cylinder has a radius of 25 ft and a height of 14 ft. What is the surface area and volume of the cylinder?
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]
How do I solve this equation?
(-4x+12)^1/2 = x
[tex](-4x+12)^{1/2}=x\\\sqrt{-4x+12}=x\\\\D:-4x+12\geq0\wedge x\geq0\\D:4x\leq12\wedge x\geq0\\D:x\leq3\wedge x\geq0\\D:x\in\langle0,3\rangle\\\\\sqrt{-4x+12}=x\\-4x+12=x^2\\x^2+4x-12=0\\x^2-2x+6x-12=0\\x(x-2)+6(x-2)=0\\(x+6)(x-2)=0\\x=-6 \vee x=2\\\\-6\not \in D\\\\\boxed{x=2}[/tex]
A copy machine makes 44 copies per minute. How long does it take to make 209 copies
Answer:
5 minutes.
44 x 5 = 220,
since 44 x 4 = 176 < 209
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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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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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]
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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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]
Logarithmic to Exponential
A=B⋅LogXC
A = 11
B = 4
C = 190
Substitute the values for A, B, and C into the logarithmic equation and solve for X.
[tex]A = B \log_x C\\\\\text{Given that,}~~ A = 11, ~B = 4~ C = 190\\\\~~~~~~~~11 = 4 \log_x (190)\\\\\implies \log_x (190) = \dfrac{11}4\\\\\implies x^{\tfrac{11}4} = 190\\\\\implies x = 190^{\tfrac 4{11}}\\\\ \implies x \approx 6.7397[/tex]
Find the 8th term of the arithmetic
sequence -2x -9,-7x - 2,
-12x + 5,...
Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used. Lewis is saving for a down payment of $8,750 on a house. The initial amount of money he has saved is $250, and the amount of money he plans on saving every month is $340. To model the situation, he created this equation, where x represents the number of months and y represents the total amount of savings: y = 250 + 340x.
The fill up for the 3rd step is y - 250 = 340x.
The fill up of the 5th step is [tex]x = \frac{y-250}{340}[/tex]The fill up of the 6th step is [tex]\frac{8750-250}{340} = 25 = x, \frac{8750-250}{340}= 34 = x[/tex]The justification for the 2nd step is subtraction PE.The justification for the 4th step is division PE.What is the simplification about?Note that:
y-250 = 250 + 340 x - 250
y = 250 + 340x.
Make x the subject of the formula:
y - 250 = 340x.
then y-250/340 = x
Then [tex]x = \frac{y-250}{340}[/tex]
The justification for the second step is subtraction property of equality because it undergoes subtraction and the collection of like terms and then subtracting them from one another as shown below:
y-250 = 250 + 340 x - 250
y= 250 + 340x - 250 + 250
Note that (-250 + 250) = 0
y = 250 + 340x.
Lastly, The fill up of the 6th step is substitution of the amount of money saved and then simplifying it.
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an isosceles trapezoid with bases 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the exact area of the trapezoid.
PLS HELP ME OUT FIRST ANSWER GETS BRAINLIEST
The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.
Height of the trapezoidThe height of the trapezoid is calculated as follows;
From the image, the sum of h1 and h2 is the height of the trapezoid.
Each of the height will be calculated using Pythagoras theorem as follows;
half of b1 = 12/2 = 6half of b2 = 16/2 = 8h1² = r² - (b1/2)²
h1² = 10² - 6²
h1² = 64
h1 = √64
h1 = 8
h2² = r² - (b1/2)²
h2² = 10² - 8²
h2² = 36
h2 = √36
h2 = 6
Total height = 8 + 6 = 14
Area of the trapezoidA = ¹/₂(b₁ + b₂)H
A = ¹/₂(12 + 16) x 14
A = 196 sq units.
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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.
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 !
how many red apple are in the jar?
Answer:
2
Step-by-step explanation:
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
Victoria bought a dress on 40% discount, and saved a massive $60. How much did the dress cost originally? How much did she pay for it?
Answer:
Answer: Original price = $150 Amount Paid = $90
Step-by-step explanation:
First we make a proportion 60/x = 40/100. When we cross multiply and divided to get x by itself we get $150 dollars. This is the original price of the dress. Now we take $150-$60 and we get $90. This is what Victoria paid for the dress after the 40% discount.
Hope this helps! :)
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]
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]
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]
Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram
The probability of drawing a black ball on the second draw will be 3/5.
How to solve the probability?From the information given, the total number of balls will be:
= 2 + 3 = 5 balls.
When the first ball is black and the second is red. This will be:
= 2/5 × 3/4
= 3/10
When the first is red and the second is black, this will be:
= 3/5 × 2/4
= 3/10
Therefore, the probability of drawing a black ball on the second draw will be:
= 3/10 + 3/10
= 3/5.
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Zoe thinks of a number. She multiplies it by 3 and adds 4. She gets the same answer when she adds 5 to the number and then multiplies the result by 2.
a. Write an equation, using n for Zoe's number.
b. Solve your equation to find Zoe's number.
Answer:
Zoe's number is 6
Step-by-step explanation:
Let the number be 'n'
a) Multiply 'n' by 3 ⇒ n*3 = 3n
Add 4 to '3n' ⇒ 3n + 4
Add 5 to 'n' ⇒ n +5
Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10
3n + 4 = 2n + 10
b) 3n + 4 = 2n + 10
Subtract 4 form both sides
3n = 2n + 10 - 4
3n = 2n + 6
Subtract 2n from both sides
3n - 2n = 6
[tex]\sf \boxed{\bf n = 6}[/tex]
Answer:
21 is probably the best answer
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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