Answer:
- x + 1
Step-by-step explanation:
(x² + 2x + 3) - (x² + 3x + 2) ← multiply terms inside parenthesis by - 1
= x² + 2x + 3 - x² - 3x - 2 ← collect like terms
= - x + 1
During a basketball season, a player scored a total of 650 points in 31 basketball games. What is his scoring average for the season?
Which of the following represents the graph of f(x) = 3x + 1? graph of exponential rising up to the right, through the point 0, 0 graph of exponential rising up to the right, through the point 0, 1 graph of exponential rising up to the right, through the point 0, 2 graph of exponential rising up to the right, through the point 0, negative 2
Answer:
Graph of exponential rising up to the right, through the point (0, 2).
Step-by-step explanation:
I think you mean f(x) = 3^x + 1.
When x = 0, 3^x = 1, so the graph of f(x) = 3^x will rise up to the right and pass through point (0. 1)
The + 1 translates the graph up 1 unit so
The graph of f(x) = 3^x + 1 passes through the point (0, 2).
Three brothers divided a prize as follows. The oldest received %, the middle brother received ½, and the youngest received the remaining $120. What was the value, in dollars, of the prize?
Answer:
1200
Step-by-step explanation:
Ok since the oldest was given 2/5, the middle was given 1/2, and the youngest was given the rest, that means the fraction that the youngest was given has to make 2/5 + 1/2 + ? = 1. So we have the equation: [tex]\frac{2}{5} + \frac{1}{2} + x = 1[/tex]. Now to add the fractions simply multiply 2/5 by 2/2 and multiply 1/2 by 5/5 To get the same denominator: [tex]\frac{4}{10} + \frac{5}{10}+x=\frac{9}{10}+x[/tex]. This means that x is 1/10 , because in adding 1/10 you get the whole 10/10. So 120 is one tenth of the entire prize. This means to get the entire prize you simply multiply by 10. This gives you the equation 120 * 10 = 1200
Volume = in2
Help me please
What is the volume
Answer: 1344
Step-by-step explanation:
Using the Pythagorean theorem, if we consider the unknown leg of the base, we get that it has a length of 12.
So, the area of the base is 96.
Multiplying this by the height, we get the volume is 1344 cubic inches.
Please help!!!!!!!!! in the similarity transformation of abc to def, abc was dilated by a scale factor of ?, reflected across the , and moved through the translation. i need help with the last portion of the question.
The complete similarity transformation is: triangle abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].
What is Similarity?When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.From the figure, we have:
AB = 2 units
DE = 4 units
So, the scale factor (k) is:
k = DE/AB
k = 4/2
k = 2
Also, both shapes are on either sides of the x-axis, and they are equidistant from the x-axis.
This means that the triangle is reflected across the x-axis with no translation.
Hence, the complete similarity transformation is: abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].
So, the scale factor is 2
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Here's a new question!
Which ray is the terminal side of a 6 radian angle in standard position?
a) positive x axis
b) positive y axis
c) negative x axis
d) negative y axis
Answer:
negative y axis
Step-by-step explanation:
6 radians is between 3pi/2 and 2pi radians, so it lies in tje fourth quadrant.
So, a terminal side is the negative y axis.
Please help! Most Beagles have shoulder heights between 36 and 41 centimeters. The following compound inequality relates the estimated shoulder height (in centimeters) of a dog to the internal dimension of the skull D (in cubic centimeters):
36 ≤ 1.02D – 31.2 ≤ 41
Which compound inequality represents the range for the skull size of Beagles? Answer choices are rounded to the nearest tenth.
Answer: B
Step-by-step explanation:
Given:
36=<1.02D-31.2<=41
Solve the compound inequality for D:
36+31.2<=1.02D<=41+31.2
67.2<=1.02D<=72.2
65.9<=D<=70.8
Therefore, option (b) is correct answer
36. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
36. x-intercept at (-2, 0) and y-intercept at (0, -3)
Answer:
The linear equation for the line with an x - intercept at (-2,0) and y-intercept at (0,-3) is found as [tex]$y=-\frac{3}{2} x-3$[/tex].
Step-by-step explanation:
A condition is given that a line has an x- intercept at (-2,0) and y - intercept at (0,-3).
It is asked to find a linear equation satisfying the given condition.
Step 1 of 2
Determine the slope of the line.
The points of the intercepts of the line are given as (-2,0) and (0,-3). Next, the formula for the slope is given as,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute -3&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 0&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{-3-0}{0-(-2)} \\m &=\frac{-3}{2} \\m &=-\frac{3}{2}\end{aligned}$$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
y=mx+b
The coordinates at the y- intercept is (0,-3). Now, as the y- coordinate is -3, so b=-3.
So, substitute -3 for b and [tex]$-\frac{3}{2}$[/tex] for m in the equation y=mx+b, and simplify to get the equation as follows,
[tex]$$\begin{aligned}&y=-\frac{3}{2} x+(-3) \\&y=-\frac{3}{2} x-3\end{aligned}$$[/tex]
This is the required linear equation.
Someone PLEASEEEEE HELP!! :(
The equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Equation of a lineFrom the question, we are to determine the equation of the line that passes through the given points
Using the formula
[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
From the give information,
[tex]x_{1} = 1 \\y_{1} = 1\\{x_{2} =5[/tex]
[tex]y_{2} = 6\\[/tex]
Putting the parameters into the formula,
[tex]\frac{y-1 }{x-1} =\frac{6-1}{5-1}[/tex]
[tex]\frac{y-1 }{x-1} =\frac{5}{4}[/tex]
∴ [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Hence, the equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
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Which table represents a linear functionWhich table represents a linear function
The table that has a constant average rate of change represents a linear function.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output of the function divided by the change in the input.
When this rate is constant, the function is said to be linear, hence the table that has a constant average rate of change represents a linear function.
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Answer:
C
Step-by-step explanation:
Which ordered pair makes both inequalities true?
y > –2x + 3
y < x – 2
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (0, 3) and (1, 1). Everything to the right of the line is shaded.
(0,0)
(0,–1)
(1,1)
(3,0)
The ordered pair which makes both inequalities true is: D. (3, 0).
How to determine ordered pair?In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.
In order to determine ordered pair which makes both inequalities true, we would substitute the points into the inequalities as follows:
At (0, 0), we have:
y > -2x + 3
0 > -2(0) + 3
0 > 3 (false).
y < x – 2
0 < 0 - 2
0 < -2 (false)
At (0, -1), we have:
y > -2x + 3
-1 > -2(0) + 3
-1 > 3 (false).
y < x – 2
-1 < 0 - 2
-1 < -2 (false)
At (1, 1), we have:
y > -2x + 3
1 > -2(1) + 3
1 > -1 (true).
y < x – 2
1 < 1 - 2
1 < -1 (false)
At (3, 0), we have:
y > -2x + 3
0 > -2(3) + 3
0 > -3 (true).
y < x – 2
0 < 3 - 2
0 < 1 (true).
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Two cards are chosen at random from a deck of 52 cards. What is the probability of
choosing a red jack at first and then choosing a red card without replacement?
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
Can someone help me please?
A chord is a part of a circle that joins two points on its circumference but does not pass through the center of the circle. From the given diagram in the question, GH = HJ. Thus the measure of chord HJ is option C. 8.6 units.
A chord is one of the parts of a circle which does not pass through its center but joins two points on its circumference. So that it is not the same as the radius of the circle.
In the given question, it has been stated that: GH and HJ are congruent.
So that by the congruency property of two lines, the length of chod GH is the same as the length of chord HJ.
Therefore, the measure of chord Hj is 8.6 units. This implies option C.
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at first decreased by 60% now increased by 80%
Answer:
72Step-by-step explanation:
at first decreased by 60% now increased by 80%
100 - 60% = 40
40 + 80% =
40 + 40 :100 * 80 =
40 + 32 =
72
A flagpole casts a shadow 22 feet long. If a man 6 feet tall cast a shadow 4.3 feet long at the same time, how tall is the flagpole? Please explain your answer.
Answer:
30.70 ft
Step-by-step explanation:
For shadow problems, we make the assumption that an object's height and its shadow length are proportional.
SetupThe proportion for the two objects is ...
height/shadow = pole/(22 ft) = (6 ft)/(4.3 ft)
SolutionMultiplying by 22 ft, we find the pole height to be ...
pole = (22 ft)(6 ft)/4.3) ≈ 30.70 ft
The flagpole is about 30.70 feet tall.
What is the slope of the line through (-1, 4) and (1, -2)?
-3 -2
3
-1
-2
-3
y
2
(1,-2)
3
4
In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure the following features are all parallel, and adjust the pattern before starting.
On this discussion board, post your answers to these questions:
1) What method(s) can Chris use to make sure the segments in the pattern are all parallel and that his new trusses are built precisely and strongly?
2) What method(s) can Chris’s boss use to verify the precision of the trusses Chris builds?
3)Identify any alternate interior angles, corresponding angles, and/or alternate exterior angles.
The method that Chris can use to make sure the segments in the pattern are all parallel is to treat AI as a single line that acts as a transversal for the lines that need to be parallel.
How to illustrate the information?Within the set of lines which need to be parallel, the acute angles must be congruent.
Both angles CDE and EDF need to be 180° minus twice the measure of one of the congruent acute angles.
The pair of the acute angles previously within each of the two sets of parallel lines are corresponding.
The fact that the transversals go through endpoints, there are no alternate angles, interior or exterior because alternate angles are on opposite sides of the transversal.
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Evaluate the expression if a = 3, b = 4, and c = 2. Simplify, if possible
a = 3, b = 4, and c = 2
a + b = c
3 + 4 = 2
3a + 4b = 2c
-4 -4
3a = -6c
3 3
a = -2
3a + 4b = 2c
-3 -3
4b = -1c
4 4
In ABC, side BC is extended to point E. When connected to vertex A, segment EA is parallel to segment BD. In this construction, you are given that BD bisects
Two triangles are said to be congruent if they have similar properties. Thus the required options to complete the paragraph proof are:
a. angle 1 is congruent to angle 2.
b. alternate angles are congruent if two parallel lines are cut by a transversal.
c. [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]
The similarity property of two or more shapes implies that the shapes are congruent. Thus they have the same properties.
From the given diagram in the question, it can be deduced that
ΔABC ≅ ΔABE (substitution property of equality)
Given that EA is parallel to BD, then:
i. <2 ≅ <3 (corresponding angle property)
ii. <1 ≅ < 4 (alternate angle property)
Thus, the required options to complete the paragraph proof are:
Angle 1 is congruent to angle 2.Alternate angles are congruent if two parallel lines are cut by a transversal.[tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]For more clarifications on the properties of congruent triangles, visit: https://brainly.com/question/1619927
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Find the value of x in the given
right triangle.
37%
X
10
X= [?]
Enter your answer as a decimal rounded to the
nearest tenth.
Enter
Answer:
x ≈ 8.0
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos37° = = ( multiply both sides by 10 )
10 × cos37° = x , thus
x ≈ 8.0 ( to the nearest tenth )
does this help? :D
Five times a number decreased by nine is equal to twice the number increased by 23. which equation could be used to solve the problem? 5x – 9 = x 23 5x – 9 = 2x 23 5x 23 2x = 23 5x 23 = 2x 23
Answer:
Step-by-step explanation:
5x-9 = 2(x+23) or 5x-9 = 2x+46
Let' x be the "number."
"Five times a number decreased by nine" means: 5x - 9
"equal to twice the number increased by 23" means: = 2(x+23)
Put them together: 5x-9 = 2(x+23)
5x-9 = 2(x+23)
5x-9 = 2x+46
[The formatting of the possible answers does not include parentheses nor algebraic symbols, making selection of a correct answer difficult. ]
By selling my car for sh 276000,the price was below the initial price. What is the initial price?
The initial price in this scenario is > sh 276000 and was therefore sold at a loss.
What is Loss?This is a situation in which the selling price of goods or services is lower than the cost price.
We were told that the selling price is sh 276000 which is less than the initial(cost) price hence he ran at a loss during the business transaction.
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Please help ill give whoever answers the best the brainliest answer :)
Answer:
The 3rd graph from the top.
Step-by-step explanation:
Just Like the story, the third graph goes up slowly and plateaus for the duration of a school day, then goes back down quicker than it went up.
The median house price in Pickering Region increased by 5.8% from Jan 1, 2019 to Jan 1, 2021. A home was purchased in Pickering Region on Jan 1, 2019 for $600,000.
a)Assume this trend continues, write an exponential equation that models the Resale Value of this home over time.
b) At this rate, determine the date when the resale price of the home would reach $1 million (Show your work to accurate to the nearest month)
c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.
Using an exponential function, we have that:
a) The equation is: [tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex].
b) The house will have a value of $1 million during the year of 2037.
c) The expected value on April 1, 2020, is of $621,520.
What is an exponential function?
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the parameters are given as follows:
A(0) = 600000, r = 0.058 each 2 years.
Hence the exponential function is:
[tex]A(t) = 600000(1 + 0.058)^{\frac{t}{2}}[/tex]
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
Item b:
It is the year 2019 + t, for which A(t) = 1000000, hence:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]1000000 = 600000(1.058)^{0.5t}[/tex]
[tex](1.058)^{0.5t} = 1.6667[/tex]
[tex]\log{(1.058)^{0.5t}} = \log{1.6667}[/tex]
[tex]0.5t\log{1.058} = \log{1.6667}[/tex]
[tex]t = \frac{\log{1.6667}}{0.5\log{1.058}}[/tex]
[tex]t = 18.12[/tex]
The house will have a value of $1 million during the year of 2037.
Item c:
April 1, 2020 is one year and 3 months = 1.25 years after January 1, 2019, hence the value of the home will be given by:
[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]
[tex]A(1.25) = 600000(1.058)^{\frac{1.25}{2}}[/tex]
A(1.25) = $621,520.
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In a group of 55 people 3x+5 people 3x+5 people like apple.If all the people who like apple also like banana and if 2x+15 people like at least one of fruit then find how many like (i) bananas only (ii) none of the fruits (iii) at most one fruit
i. 20 people
ii. 3 people
iii. 26 people
How to determine the valuesWe have that;
3x + 5 people likes apples
3x + 5 people likes banana
2x + 15 people likes at least one of the fruits
The total number of people = 55
Let's find the value of x
3x + 5 + 2x + 15 = 55
5x + 20 = 55
5x = 55 - 20
5x = 35
x = 35/5
x = 7
i. People that likes banana only = 3x + 5 = 3 × 5 + 5 = 15 + 5 = 20 people
ii. None of the fruits = 55 - 2x + 15 = 55 - 3x + 5 - 3x + 5 = 55 - 26 +26
= 55 - 52
= 3 people
iii. At most one fruit = 55 - 2x + 15 = 55 - 2(7) + 15 = 55 - 29 = 26 people
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Help please I will mark brainliest
(a) Using Fermat's little theorem, show that 999 999 is divisible by 7.
(b) A number has digits that are all 9 and is divisible by 13. Show that
it is also divisible by 1001.
(a) Fermat's little theorem states that for any prime [tex]p[/tex], we have
[tex]a^{p-1} \equiv 1 \pmod p[/tex]
for any integer [tex]a[/tex]. Then
[tex]999,999 \equiv 1,000,000 - 1 \equiv 10^6 - 1 \equiv 1 - 1 \equiv 0 \pmod 7[/tex]
so 7 does indeed divide 999,999.
(b) Generalizing, we have
[tex]10^{12n} - 1 \equiv \underbrace{999\ldots999}_{12n \text{ nines}} \equiv (10^n)^{12} - 1 \equiv 0 \pmod {13}[/tex]
for positive integer [tex]n[/tex]. Now, since 1 = 1001 - 1000 and [tex]-1\equiv1000\pmod{1001}[/tex], it follows that [tex]10^3[/tex] is its own inverse modulo 1001, i.e.
[tex]10^3 x \equiv 1\pmod{1001} \implies x = 10^3[/tex]
This means
[tex]10^{12n} \equiv (10^3\times10^3)^{2n} \equiv 1^{2n} \equiv 1\pmod{1001} \\\\ \implies 10^{12n} - 1 \equiv 0 \pmod{1001}[/tex]
which is what we wanted to show.
prove the diagonals of a square are perpendicular
Answer:
Given :- ABCD is a square.
To proof :- AC = BD and AC ⊥ BD
Proof :- In △ ADB and △ BCA
AD = BC [ Sides of a square are equal ]
∠BAD = ∠ABC [ 90° each ]
AB = BA [ Common side ]
△ADB ≅ △BCA [ SAS congruency rule ]
⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]
In △AOB and △AOD
OB = OD [ Square is also a parallelogram therefore, diagonal of parallelogram bisect each other ]
AB = AD [ Sides of a square are equal ]
AO = AO [ Common side ]
△AOB ≅ △ AOD [ SSS congruency rule ]
⇒ ∠AOB = ∠AOD [ Corresponding parts of congruent triangles are equal]
∠AOB + ∠AOD = 180° [ Linear pair ]
∠ AOB = ∠AOD = 90°
⇒ AO ⊥ BD
⇒ AC ⊥ BD
Hence proved, AC = BD and AC ⊥BD
Construct a matrix of order 3×2 whose elements are given by Cij=|−2i+3j|/2
[tex]C_{ij}[/tex] is the entry of [tex]C[/tex] in row [tex]i[/tex] and column [tex]j[/tex]. [tex]C[/tex] has 3 rows and 2 columns, so
[tex]C_{11} = \dfrac{|-2\times1+3\times1|}2 = \dfrac{|-2+3|}2 = \dfrac{|-1|}2 = \dfrac12[/tex]
[tex]C_{12} = \dfrac{|-2\times1+3\times2|}2 = \dfrac{|-2+6|}2 = \dfrac{|4|}2 = 2[/tex]
[tex]C_{21} = \dfrac{|-2\times2+3\times1|}2 = \dfrac{|-4+3|}2 = \dfrac{|-1|}2 = \dfrac12[/tex]
[tex]C_{22} = \dfrac{|-2\times2+3\times2|}2 = \dfrac{|-4+6|}2 = \dfrac{|2|}2 = 1[/tex]
[tex]C_{31} = \dfrac{|-2\times3+3\times1|}2 = \dfrac{|-6+3|}2 = \dfrac{|-3|}2 = \dfrac32[/tex]
[tex]C_{32} = \dfrac{|-2\times3+3\times2|}2 = \dfrac{|-6+6|}2 = \dfrac{|0|}2 = 0[/tex]
Then the matrix is
[tex]C = \begin{bmatrix}\dfrac12 & 2 \\\\ \dfrac12 & 1 \\\\ \dfrac32 & 0\end{bmatrix} = \dfrac12 \begin{bmatrix}1&4\\1&2\\3&0\end{bmatrix}[/tex]
A researcher designs a study that will investigate the effects of a new
statistical software on graduate students' understanding of statistics. The
researcher creates a survey, consisting of 10 questions. She compares two
samples, each containing 10 randomly selected students. One sample
consists of students graduating in May. The other sample consists of
students graduating the following May.
A. The sample size is too small.
B. One sample has more graduate level experience than the other
sample.
C. An exam should be used, instead.
D. Randomly selected students were used.
The statement that is true is: D. Randomly selected students were used.
What is survey?Survey can be defined as the data or information that a researcher or research analyst collected from a population so as to reach or draw a conclusion.
Based on the scenario the student were randomly selected which means that the randomly selected students were used to conduct the survey.
Therefore the correct option is D.
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What type of number is −0.5/ −0.5
Choose all answers that apply:
a)Whole number
b)Integer
c)Rational
d)Irrational
Answer:
[tex] \frac{ - 0.5}{ - 0.5} = 1 \\ [/tex]
1 is a whole number, an integer, and rational.
Step-by-step explanation:
HOPE THIS HELPS.