The correct statement is:
"She is not correct because she did not substitute the same number in both expressions in Step 1."
Is Sophia correct?First, let's see if Sophia is correct.
She starts with the expression:
-(4x - 5) + 2*(x - 3) = -2x - 5
Expanding the left side:
-4x + 5 + 2x - 6 = -2x - 5
-2x -1 = -2x - 5
So the constant term is different.
Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).
"She is not correct because she did not substitute the same number in both expressions in Step 1."
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Une fonction polynomiale du second degré possède les caractéristiques
suivantes :
• La fonction est croissante sur l'intervalle [0, 8].
• La fonction est décroissante sur l'intervalle ]-10, 0].
• La courbe passe par le point (-8, 4).
PSST
↓
Voici les symboles dont tu pourrais avoir besoin dans ta réponse. N'hésite pas à
les copier-coller à partir d'ici si tu ne les trouves pas sur ton clavier.
[]%
SAVOIR-FAIRE
INDICE
Représente graphiquement la fonction, puis détermine son codomaine. Utilise la
notation décimale au besoin.
Le codomaine est.
Je n’arrive pas à trouver le co domaine si quelqu’un peut m’aider svp?
A second-degree polynomial takes the form
[tex]f(x) = ax^2 + bx + c[/tex]
for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.
Differentiating f(x) with respect to x gives
[tex]\dfrac{df}{dx} = 2ax + b[/tex]
We're told that
• f(x) is increasing on [0, 8]
• f(x) is decreasing on ]-10, 0]
and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write
[tex]f(x) = ax^2 + c[/tex]
We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint
[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]
Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so
[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]
This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.
Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,
a = 1, c = -60 ⇒ f(x) = x² - 60 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}
a = 2, c = -124 ⇒ f(x) = 2x² - 124 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}
etc.
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
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 rational functions is graphed below
The answer should be A. :)
The correct rational function of the graph is,
⇒ f (x) = 1 /(x + 5)²
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph is shown in fgigure.
Now, By graph of function,
The graph is not defined at x = - 5.
Hence, From equation (i);
⇒ f (x) = 1 /(x + 5)²
Clearly, Function is noy defined at x = - 5.
Hence, The correct rational function of the graph is,
⇒ f (x) = 1 /(x + 5)²
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what is the slope of the line shown below?
Answer:
C. 2
Step-by-step explanation:
Gradient = [tex]\frac{change in y}{change in x}[/tex]
Gradient = [tex]\frac{6}{3}[/tex]
Gradient = 2
A Each topping costs $1
B With no toppinga a pizza costs $14
C With no toppings a pizza costs $6
D Each topping costs $6
A four-sided shape has four congruent angles and sides. Which quadrilateral could it be? A. quadrilateral B. trapezoid C. square D. parallelogram
Answer:
square
Step-by-step explanation:
Option A is also correct somehow
These things can be possible in three optionsquadrilateral (Off course)ParallelogramSquarebut we are not sure about first 2 if they have equal sides or angles
only square have each angle 90 and all sides equal
So Option C is correct
Answer:
C. square
Step-by-step explanation:
Congruent means "the same" (having the same shape and size).
Any four-sided, 2-dimensional shape with straight sides is called a quadrilateral.
There are 6 special types of quadrilaterals:
Rectangle
Opposite sides are parallel and equal in lengthAll interior angles are 90°Square
All sides are equal in lengthAll interior angles are 90°Rhombus
All sides are equal in lengthOpposite sides are parallelOpposite angles are equalParallelogram
Opposite sides parallel and equal in lengthOpposite angles are equalTrapezoid
One pair of opposite parallel sidesIsosceles Trapezoid
One pair of opposite parallel sidesOne pair of non-parallel sides equal in lengthTwo pairs of equal base anglesKite
Two pairs of adjacent sides equal in lengthThe angles included between the sides of differing lengths are equalConclusion
A four-sided shape that has four congruent angles and sides is a SQUARE.
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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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]
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! :)
Drag the tiles to the boxes to form correct pairs.
Match the cube roots and square roots with their values.
Drag the tiles to the boxes to form correct pairs.
Match the cube roots and square roots with their values.
Match the cube roots and square roots with their values.
Match the cube roots and square roots with their values.
Match the cube roots and square roots with their values.
The match up are:
√4 = 2∛27 = 3√64 = 8∛64 = 4√49 = 7∛1000 = 10What is square root?The square root, in mathematics is known to be the factor of a number that, is said to be multiplied only by itself and thus it gives the original number.
For example:
[tex]\sqrt{4}[/tex] will give you 2.
Therefore, The match up are:
√4 = 2∛27 = 3√64 = 8∛64 = 4√49 = 7∛1000 = 10Learn more about cube roots from
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p + 46 = 94, what is p?
48.
Because 46+48 equals 94.
You can easily find out equations to this by subtracting the 46 from 94 to see what p is equal to.
HAVE A NICE DAY!
Given the function h(x)=-5 √x, which statement is true about h(x)?
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (–∞, 0).
The function is decreasing on the interval (0, ∞).
The function is increasing on the interval (0, ∞).
The true statement about h(x) is (c) the function is decreasing on the interval (0, ∞)
How to interpret the function?The function is given as:
h(x) = -5√x
Next, we plot the graph of the function h(x)
From the attached graph, we can see that:
As x increases from 0, the function value decreases
Hence, the true statement about h(x) is (c) the function is decreasing on the interval (0, ∞)
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I have no clue on this one either
Answer:
Area of the triangle = 210 cm^2 .
Step-by-step explanation:
Perimeter of triangle = 4x + 1 + 3x - 1 + 3x = 70
10x = 70 - 1 + 1 = 70
x = 7.
Area A = 1/2 * base * height
= 1/2 * 3x * (3x - 1)
= 1/2 * 3(7) * (3(7) -1)
= 1/2 * 21 * 20
= 210.
Which of the following quadrilaterals must be a parallelogram according to the minimum criteria?
Answer: All of them are correct I think
Step-by-step explanation:
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]
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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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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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]
-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
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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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 !
Calculus. Factor the given polynomial.
Answer:
X=-2 or x=-7
Step-by-step explanation:
(x+2)(x+7)=0
X=-2 or x=-7
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]
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
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]
how many red apple are in the jar?
Answer:
2
Step-by-step explanation: