The vertex is [tex](-1,1)[/tex]
Explanation:
The equation is [tex]f(x)=2x^{2} +4x+3[/tex]
To find the vertex, we need the equation in the form of [tex]f(x)=a (x-h)^{2}+k[/tex]
Dividing each term by 2 in the equation [tex]f(x)=2x^{2} +4x+3[/tex]
[tex]f(x)=2(x^{2} +2x+\frac{3}{2} )[/tex]
Now, completing the square by adding and subtracting 1, we get,
[tex]f(x)=2(x^{2} +2x+1-1+\frac{3}{2} )[/tex]
The first three terms can be written as [tex](x+1)^{2}[/tex],
[tex]f(x)=2[(x+1)^{2}+\frac{1}{2} ][/tex]
Multiplying 2 into the bracket, we get,
[tex]f(x)=2(x+1)^{2} +1[/tex]
This equation is of the form [tex]f(x)=a (x-h)^{2}+k[/tex]
Now, we shall find the vertex [tex](h,k)[/tex]
Thus, [tex]h=-1[/tex] and [tex]k=1[/tex]
Thus, the vertex is [tex](-1,1)[/tex]
Mr Edwards buys 2 new knobs for each of his kitchen cabinets. How many knobs does he buy?
Answer:
Step-by-step explanation:
You need to find out how many cabinets it is
Final answer:
To determine how many knobs Mr. Edwards needs to buy for his kitchen cabinets, we need to know the total number of cabinets since he needs 2 knobs for each cabinet.
Explanation:
Mr. Edwards wants to buy new knobs for his kitchen cabinets. To determine how many knobs he needs to buy, we would need to know the exact number of kitchen cabinets he has. However, the information about Chelsea and her trip to Europe, her being a shop-a-holic and physics lover, and the estimation of the number of pairs of shoes that can fit in her closet seem to be unrelated to Mr. Edwards's question. Therefore, to answer Mr. Edwards's query, we need the number of cabinets to calculate the total number of knobs. If there are X cabinets, Mr. Edwards would need to purchase 2X knobs.
J divided by 9 is 5 j equal
Answer:
J= 45
Step-by-step explanation:
j ÷ 9 = 5
×9. ×9
J= 45
you multiply by to cancel out the nine. you do it on both sides of the equal sign so it's proportionate
Answer:
j=45
j/9=5
Step-by-step explanation:
j equals fourty five
j over or divided (by) nine equals five
How many times does 9 go into 143
Answer:
143/9 = 15.89
Step-by-step explanation:
Help!! brainliest
Lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a figure for this relationship.
Answer:
B
Step-by-step explanation:
Linc c moving upward will intersect line b
Option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
Lines a, b, and c are coplanar. Lines a and b intersect.
Line c intersects only with line b
As we can see in the picture, the lines are given:
As we know, the coplanar plane is the plane in which all lines or points lie (ie. in the same plane) known as coplanar.
In option (B) the lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.
Thus, option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.
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In the graph of an inequality, the region below a dashed line through the points (4, 3) and (0, 2) is shaded. What inequality does the graph represent?
Answer:
The inequality that represents the graph is y < [tex]\frac{1}{4}[/tex]x + 2
Step-by-step explanation:
i) the region below a dashed line through the points (4,3) and (0,2) is shaded.
ii) first we find the equation of the line passing through the points (4,3) and (0,2)
(y - 3) = [tex](\frac{3 - 2}{4 - 0})[/tex](x - 4) ⇒ y - 3 = [tex]\frac{1}{4}[/tex](x - 4)
⇒ 4y - 12 = x - 4 ⇒ 4y = x + 8 ⇒ y = [tex]\frac{1}{4}[/tex]x + 2
iii) for the area shaded below the line whose equation is given in ii) above the inequality that will represent the shaded region is given by
y < [tex]\frac{1}{4}[/tex]x + 2
The graph represents the inequality y < 1/4x + 2. The inequality was calculated based on the information given: points the line goes through, shading below the line, and the line being dashed all determine the inequality's form.
Explanation:To determine the inequality graphed, we first need to find the equation of the line. The line passes through the points (4, 3) and (0, 2), so we can use these points to find the slope of the line.
The formula for the slope (m) is [tex](y2 - y1)/(x2 - x1).[/tex]. Plug in the coordinates of the two points into this formula: ([tex]3 - 2) / (4 - 0) = 1/4[/tex] So, our slope is 1/4.
Given a slope (m) of 1/4 and the y-intercept (b) of 2, we can write the equation of the line in slope-intercept form (y = mx + b) as y = 1/4x + 2.
One key part of your question is that the region below this line is shaded. In the language of inequalities, shading below the line corresponds to 'y is less than' the line's equation. Also, the line is dashed, meaning that the points on the line are not included in the solution, which we denote as 'less than' rather than 'less than or equal to'.
So, the inequality represented by this graph is y < 1/4x + 2.
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the greatest common factor 10z-40
Answer:
10 is the greatest common factor
Step-by-step explanation:
Find the prime factors of each term in order to find the greatest common factor (GCF).
10
4 cubed 2 divided by 4
Answer: 32
Step-by-step explanation:
4 cubed 2 divided by 4
Simply is
4 to the power 3 multiplied by 2 divided by 4
4*4*4*2/4
128/4= 32
A bag of Chocolates is labeled to contain 0.384 pounds of chocolate the actual weight of the chocolate is 0.3798 pounds. How much have you or lighter are the chocolates and The started on the label. Show your reasoning
Answer:
The actual weight is 1.1% less (100 - 98.9) than the labeled weight.
Step-by-step explanation:
1. Let's review the information given to us to answer the question properly:
Labeled weight of the bag of chocolates = 0.384 pounds
Actual weight of the bag of chocolates = 0.3798 pounds
2. How much have you or lighter are the chocolates and the stated on the label. Show your reasoning.
Let's find how much we have comparing the labeled weight and the actual weight, using a Direct Rule of Three, this way:
Weight Percentage
0.384 100 %
0.3798 x %
0.384x = 0.3798 * 100
0.384x = 37.98
x = 37.98/0.384
x = 98.9 (Rounding to one decimal place)
The actual weight is 1.1% less (100 - 98.9) than the labeled weight.
The chocolates are 0.0042 pounds lighter than what is stated on the label.
Explanation:The difference in weight between the labeled weight and the actual weight of the chocolates is 0.0042 pounds. This means that the chocolates are 0.0042 pounds lighter than the label indicates.
To calculate this, subtract the actual weight from the labeled weight: 0.384 - 0.3798 = 0.0042 pounds.
So, the chocolates are 0.0042 pounds lighter than what is stated on the label.
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Next in sequence 3, 9, 27, _?
Answer: +81
Explanation: To find the next term in the pattern, begin by studying the pattern. Here, notice that 3 x 3 is equal to 9 and 9 x 3 is equal to 27.
Continuing the same pattern, 27 x 3 is equal to 81.
So the next term in the pattern is +81.
What is the best definition of arithmetic
Answer:
1a : a branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them. b : a treatise on arithmetic. 2 : computation, calculation.
Step-by-step explanation:
Final answer:
Arithmetic is a branch of mathematics dealing with numbers, including operations like addition, subtraction, multiplication, and division; it is recognized for its universality and foundational importance in various fields of study.
Explanation:
Arithmetic is a fundamental branch of mathematics that involves the study and manipulation of numbers. It includes the basic operations of addition, subtraction, multiplication, and division. These operations are essential for understanding and working with numbers in both simple and complex mathematical contexts, such as the calculation of quantities, relationships, and patterns. Arithmetic is universally acknowledged for its constant and indubitable truths, such as two plus three always equalling five. This branch of mathematics is not only vital in academic settings but is also crucial in everyday decisions and processes regardless of the period or location. Arithmetic serves as the basis for more advanced mathematical studies and is woven intricately into various fields such as physics, astronomy, and engineering, highlighting its foundational importance in the sciences and beyond.
The length of a rectangle is 6 inches more than it’s width. if the perimeter of the rectangle is 24 inches, find the dimensions. create let statement and write equation.
Answer:
The dimensions of the rectangle are;
Width = 3 inches
Length = 9 inches
Step-by-step explanation:
Given;
Perimeter of the rectangle is 24 inches Length is 6 inches more than the widthWe want to determine the dimensions of the rectangle;
Let the width of the rectangle be x inchesThis means, the length of the rectangle will be (x+6) inchesBut, Perimeter = 2(L+W)Forming an equation, we get;
2 ( x + x + 6) = 24
4x + 12 = 24
With the equation we can solve for x
4x = 24 - 12
4x = 12
x = 3
and (x + 6) = 9
Therefore;
Width = 3 inches
Length = 9 inches
The width of the rectangle is 3 inches and the length is 9 inches.
Let's assume that the width of the Rectangle dimensions is represented by 'w' inches.
Since the length is 6 inches more than the width, we can represent it as 'w + 6' inches.
The perimeter of a rectangle is the sum of all its sides.
In this case, the formula for the perimeter is 2(w + l), where w represents the width and l represents the length.
So, for this problem, we have the equation 2(w + w + 6) = 24.
Simplifying this equation, we get 4w + 12 = 24.
Solving for 'w', we find that the width is 3 inches.
Plugging this value back into the equation for the length, we find that the length is 9 inches.
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What is this percent of change, i'm confused? 1/4 to 1/8
Answer:
Step-by-step explanation:
Percent change= (1/4-1/8)/1/4 × 100%
= {(2 -1)/8} ÷ 1/4 × 100%
= (1/8 ÷ 1/4) × 100%
= 1/8 × 4/1 × 100%
=1/2 × 100%
= 50%
It is 50% change
Answer:
I believe the answer is 50%.
1/4 x 1/2 = 0.125
125/1000
125/1000 <-- divide numerator and denominator by 125
the above fraction simplifies to 1/8
So, one 1/4 is double the value of one 1/8
1.) Write f(x) = x2 - 6x + 8 in vertex form
Answer:
f(x) = (x - 3)² - 1
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
Add/subtract ( half the coefficient of the x- term )² to x² - 6x
f(x) = x² + 2(- 3)x + 9 - 9 + 8
= (x - 3)² - 1
2.5 lb equals how many cups
You can't really convert that becasue cups is a volume and pounds is a weight. If I have a cup of feathers and a cup of iron filings, then the iron filings will weigh much less than the feathers. A cup different items would not have the same weight - if you know what I mean.
Over the last 5 business days, Ross made the following numbers of sales calls: 7,9,6,10, and 8. On average, how many calls
did he make a day?
Answer : 8
7 + 9 + 6 + 10 + 8 = 40
40/5 (5 is the number of sales calls) = 8
can someone help me with this problem please
Answer:
The correct option is third one m∠2 =106° , m∠3 =37°.
Therefore,
[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]
Step-by-step explanation:
Given:
Consider ABCD as a Rhombus such that,
∠A = ∠1 = 106°
∠C = ∠2
∠BDC = ∠3
AB=BC=CD=DA
To Find:
∠2 = ?
∠3 = ?
Solution:
ABCD is a Rhombus
∠A ≅ ∠C ............opposite angles of Rhombus are equal. ( property )
Substituting the values we get
∠1 = ∠2
But ∠1 = 106°
∴ ∠2 = 106° ....... Transitive property,
As BC = CD ...Given
ΔBCD is an Isosceles triangle
∴ ∠CBD ≅ ∠BDC = ∠3 ........base angle of Isosceles triangle are congruent.
we know that in a triangle,
Sum of measures of all angles is 180°
in Triangle BCD
[tex]\angle 3 +\angle 2 +\angle 3 =180[/tex]
Substituting the values we get
[tex]2m\angle 3 =180-106=74\\\\\angle 3=\dfrac{74}{2}=37\\\\m\angle 3 = 37\°[/tex]
Therefore,
[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]
32 mm
16 mm
es
Given that the two figures are similar, use a scale factor to find the missing length b.
8 mm
12 mm
16 mm
24 mm
Answer:
scale factor is 4 so it will be 8mm
Does this Series Converge or Diverge? What is the common ratio?
Answer:
Converge
Step-by-step explanation:
Given geometric series
[tex]1,000+200+40+8+\dfrac{8}{5}+...[/tex]
The first term of this geometric series is [tex]a_1=1,000.[/tex]
Next terms can be obtained by dividing by 5 or multiplying by [tex]\frac{1}{5}:[/tex]
[tex]a_2=1,000\cdot \dfrac{1}{5}=200\\ \\a_3=200\cdot \dfrac{1}{5}=40\\ \\a_4=40\cdot \dfrac{1}{5}=8\\ \\a_5=8\cdot \dfrac{1}{5}=\dfrac{8}{5}\\ \\...[/tex]
The sum of this infinite geometric series is
[tex]S=\dfrac{a_1}{1-q}=\dfrac{1,000}{1-\frac{1}{5}}=\dfrac{1,000}{\frac{4}{5}}=1,250[/tex]
Hence, this series is convergent
Given ΔFGH ~ ΔLMN, which must be true? Select all that apply.
A. FGLM=FHLN
B. FH ~ LN
C. m∠Fm∠L=m∠Gm∠M
D. GH≅MN
E. m∠H≅m∠N
In similar triangles ΔFGH and ΔLMN, only the corresponding angles are congruent (thus ∠H ≅ ∠N). The sides are proportionate, not necessarily congruent. Other listed options are either incorrect or unclear due to potential misinterpretations or typographical errors.
Explanation:Given that triangles ΔFGH and ΔLMN are similar (ΔFGH ~ ΔLMN), the following must be true based on the concept of similar triangles:
The corresponding angles are congruent, which means that ∠F ≅ ∠L, ∠G ≅ ∠M, and ∠H ≅ ∠N (option E). The corresponding sides are proportionate, meaning that the ratio of corresponding sides (FG/LM, GH/MN, and FH/LN) are equal. However, this doesn't mean that the corresponding sides are congruent. Hence option D is not necessarily true. Option B implies that lines FH and LN are similar, which is not a concept in geometry. Hence it's incorrect. Option A is incorrect because it seems to imply congruence of some unspecified aspect of the triangles, which is not a guaranteed condition under triangle similarity. Option C's meaning is unclear due to potential typographical error or misinterpretation.Learn more about Similar Triangles here:
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Of the 8 planets is our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as topic for a report, what is the probability that the selected planet will be rocky
Answer:
50%
Step-by-step explanation:
He has a 4/8 that he picks a rocky and a 4/8 that he doesn't. That gives us 1/2 and 1/2. 1/2=0.5 0.5×100%=50%
in the following triangle, what is the length of the hypotenuse, please answer quickly please
Answer:
6
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{2} }{hyp}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
hyp = 3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 3 × 2 = 6
The solution to which inequality is graphed below?
Answer:
D
Step-by-step explanation:
6b>-18
b>-3
This is shown by the line going from -3 into infinity.
Answer:
6b > -18
Step-by-step explanation:
[tex]6b > -18 \\then \\b >\frac{-18}{6} \\then\\b > -3[/tex]
A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?
The population of the town in 5 years is 12763
The given parameters are:
Initial value (a) = 10000
Rate (r) = 5%
A population growth model is represented as:
[tex]y = a(1 + r)^x[/tex]
So, we have:
[tex]y = 10000 * (1 + 5\%)^x[/tex]
In 5 years, we have:
[tex]x = 5[/tex]
So, we have:
[tex]y = 10000 * (1 + 5\%)^5[/tex]
Evaluate
[tex]y = 12763[/tex]
Hence, the population in 5 years is 12763
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Rachel ordered early learning software for her daughter from an online retailer. Each item costs
$7.50, and there is a shipping fee of $7.50 for the entire order.
9. What is the cost of Rachel's order if she buys 7 items?
Answer:
60$
Step-by-step explanation:
Shipping is 7.50 and the 7 items are 52.5 total
In AABC, mZA=x, mZB = 2x +2, and
m_C= 3x +4. What is the value of x?
1) 29
2) 31
3) 59
4 61
Answer:
x = 29
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
x + 2x + 2 + 3x + 4 = 180, that is
6x + 6 = 180 ( subtract 6 from both sides )
6x = 174 ( divide both sides by 6 )
x = 29
What is the answer of (1, 9); slope 4 on a graph?
The point (1, 9) with a slope of 4 on a graph corresponds to the answer of 13.
Explanation:The answer is 13.
To calculate this, we use the formula for the equation of a straight line: y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = 4x + 9. Substituting x = 1 into the equation gives y = 4(1) + 9 = 13.
Therefore, the point (1, 9) has a slope of 4 on the graph.
This figure is made up of a rectangle and parallelogram.
What is the area of this figure?
Enter your answer in the box. Do not round any side lengths.
The area of the figure is 40 units. (rounded off from 39.998 units)
Step-by-step explanation:
1. Area of the figure = Area of Rectangle + Area of Parallelogram.
2. Naming points:
Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).
Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).
3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.
In simple words, in A(-6,1), x' = -6; y' = -1
4. Formula for finding area:
Area of a rectangle = length (l) × width (w)
Area of a parallelogram = base (b) x height (h)
5. Finding area of the rectangle:
l = AD = [tex]\sqrt{[x'''' - x']^{2} - [y'''' - y']^{2}}[/tex]
, i.e. AD = [tex]\sqrt{[2 - (-6)]^{2} - [1 - (-1)]^{2}}[/tex]
, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l
Now, w = AB = [tex]\sqrt{[x'' - x']^{2} - [y'' - y']^{2}}[/tex]
, i.e. AB = [tex]\sqrt{[(-5) - (-6)]^{2} - [(-5) - (-1)]^{2}}[/tex]
, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w
Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.
6. Finding area of the parallelogram:
b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)
h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.
Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.
7. Now, adding both, we can arrive at the final answer.
Area of the figure = Area of rectangle + Area of parallelogram,
i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)
consider quadrilateral ABCD and point E in the figure below. graph r(135°, E) (ABCD). which graph shows the pre-image ABCD and the image A’ B’ C’ D’ ?
The graph which shows the pre-image of quadrilateral ABCD and the image A’ B’ C’ D’ after the rotation is graph number 1.
What is rotation of figure?Rotation of a figure is the transformation of it about a point in either clockwise or anticlockwise direction.By rotating, a figure changes the point of the figure.
The quadrilateral ABCD and point E in the graphed in the figure below. This quadrilteral is rotated r(135°, E) in order to construct quadrilteral A’ B’ C’ D’ .
The rotation of the figure is 135 degrees. This angle can be break as,
[tex]\theta=135\\\theta=90+45[/tex]
The angle is rotated 90 and 45 degrees. To rotate 90 degree, the angle must be flliped 90 degree clockwise from point E keeping the point c at center.
After this the 45 degree more the figure is rotated. This is shown accurately in the figure A.
Thus, the graph which shows the pre-image of quadrilateral ABCD and the image A’ B’ C’ D’ after the rotation is graph number 1.
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What is the answer to -2/3x4
Answer
-8/3 (fraction)
or in decimal form it would be -2.6 (the six would be repeating)
Step-by-step explanation:
25 points. Math question
Answer:
-8
Step-by-step explanation:
I believe it is -8
first you 2(-2) - 4
then you -4 -4= -8
Hope that was helpful.
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]f(x) = 2x - 4 \\ f( - 2) = {?} \\ \\ x = - 2 \\ \\ f( - 2) = 2( - 2) - 4 \\ f( - 2) = - 4 - 4 \\ f( - 2) = - 8[/tex]
=> The answer is -8.