Graph the line with the given slope that passes through the given point.
(a) slope:
3
4
,
point:
(1, 5)
Answers
The linear equation can be written as:
y = (3/4)*x + 17/4
And the graph can be seen at the end.
How to graph the linear equation?
A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we have the slope m = 3/4, so we get:
y = (3/4)*x + b
And the line passes through (1, 5), replacing these values in the equation we get:
5 = (3/4)*1 + b
5 - 3/4 = b
20/4 - 3/4 = b
17/4 = b
So the linear equation is:
y = (3/4)*x + 17/4
To graph the line we need other point, if we use x = 0 we get:
y = (3/4)*0 + 17/4 = 17/4
Then we have the points (1, 5) and (0, 17/4).
To graph the line, we just need to find these two points and connect them with a line, the graph can be seen below.
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Related Questions
A triangle is placed in a semicircle with a radius of , as shown below. Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Solution:
Given the figure below:
The area of the shaded region is expressed as
[tex]area\text{ of shaded region = area of semicircle - area of triangle}[/tex]step 1: Evaluate the area of the semicircle.
The area of the semicircle is expressed as
[tex]\begin{gathered} area\text{ of semicircle=}\frac{1}{2}\times\pi r^2 \\ where\text{ r is the radius of the circle} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of semicircle = }\frac{1}{2}\times3.14\times4cm\times4cm \\ \Rightarrow area\text{ of semicircle =25.12 cm}^2 \end{gathered}[/tex]step 2: Evaluate the area of the triangle.
The area of the triangle is expressed as
[tex]\begin{gathered} area\text{ of triangle =}\frac{1}{2}\times base\times height \\ thus,\text{ we have} \\ area\text{ of triangle =}\frac{1}{2}\times8cm\times4cm \\ =16\text{ cm}^2 \end{gathered}[/tex]step 3: Evaluate the area of the shaded region.
Recall that
[tex]\begin{gathered} area\text{ of shaded reg}\imaginaryI\text{on = area of sem}\imaginaryI\text{c}\imaginaryI\text{rcle- area of tr}\imaginaryI\text{angle} \\ \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of shaded region = \lparen25.12 -16\rparen cm}^2 \\ =9.12\text{ cm}^2 \end{gathered}[/tex]Hence, the area of the shaded region is
[tex]9.12\text{ cm}^2[/tex]let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)
Answers
k(x)=3h(x)+4x^4/g(x). given the following table of values, k'(-1) will be 3.
What is differentiation?A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative. the procedure for determining a function's derivative, or rate of change, in mathematics. Differentiation is the method used to calculate a function's derivative. The derivative is the rate at which two variables, x and y, change relative to one another.
Given Data
k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]
k(x) = -3h'(x) + 4[tex]\frac{4x^{3} g(x)- x^{4}g'(x) }{gx^{2} }[/tex]
k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g(-1)}{g(-1)^{2} }[/tex]
k'(-1) = -3(-1) + 4(0)
k(-1) = 3 + 0
k'(-1) = 3
k(x)=3h(x)+4x^4/g(x). given the following table of values, k'(-1) will be 3.
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Graph the line y= 3x - 5 using the slope and y-intercept.
Step-by-Step Solution
Step 1: Identify the slope and y-intercept of the line.
y = 3x-5
The slope is m = 1.
(Type an integer or a fraction.)
Answers
The required slope m is 3 and the y-intercept is - 5.
What is a y-intercept?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Given : The line y = 3x - 5
This is of the form y = mx + c which is the equation of the line.
On comparing these two equations
Thus the slope is 3 .
And y intercept is :
y = 3x - 5 and when x = 0
y =- 5.
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calculate the mean of each data set below. can you find any shortcuts that allow you to find the mean without having to d much calculation
a. 6, 10, 6,10
b. 11, 12, 12, 13, 12
c 0, 5, 4, 8, 0, 7
Answers
b: 24 + 36 = 60 and 60/5 = 12
c: 12 + 12 = 24 and 24/6 = 4
True or false?
By issuing a patent, the government can give a company monopoly power.
Answers
Answer:
this is true
Step-by-step explanation:
counselor at a summer camp are assigned beds to the campers Jackson is assign a bed and then Eva is assigned one are these two events dependent or independent
Answers
Solution;
The events are independent
Write a specific formula to describe the variation: Q varies jointly with the square of the inverse of the sum of b and R; Q = 4 when b = 2, R = 8.
Answers
Given the following variation
[tex]Q\propto\frac{1}{(b+R)^2}[/tex]Introducing the constant of proportionality c as shown below
[tex]\begin{gathered} Q=c\times\frac{1}{(b+R)^2} \\ Q=\frac{c}{(b+R)^2} \end{gathered}[/tex]Q=4, when b=2, R= 8
Let use the above values of Q, b, and R to find the value of c as shown below:
[tex]\begin{gathered} 4=\frac{c}{(2+8)^2} \\ 4=\frac{c}{10^2} \\ 4=\frac{c}{100} \\ c=4\times100 \\ c=400 \end{gathered}[/tex]Let us substitute c in the formula as shown below
[tex]Q=\frac{400}{(b+R)^2}[/tex]Hence, the specific formula to describe the variation is
Q= 400/(b+R)²
Ron's Tea Shop has caffeinated tea and decaffeinated tea. During the lunchtime rush, the tea shop served 25 teas in all, 20% of which were caffeinated. How many caffeinated teas did the tea shop serve?
Answers
The number of caffeinated teas that the tea shop serve is 5.
How to calculate the percentage?Number of teas served = 25 teas.
Percentage that was caffeinated.= 20%
Therefore the number that was caffeinated will be the percentage multiplied by the number of teas. This will be:
= 20% × 25
= 0.2 × 25
= 5
Therefore, 5 are caffeinated
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If g(x)=5x, h(x)=√x, find the composition.
(g . h)(0)
( g . h ) ( 0 ) = _____
Answers
The value of the composition (g . h)(0) is 0
What is a function?A function can be defined as a mathematical law, expression of rule that explains the relationship between two variables in an equation.
These variables are;
The independent variableThe dependent variableThe functions are;
g(x) = 5xh(x) = √xThe composite function is gotten by substituting the value of x of the independent variable in the function.
The composite function (g . h)(0) is determined by substituting the value of x as h(x) in the function g(x), we get;
(g . h) = 5√x
Now, substitute the value of x as 0, we have;
(g . h)(0) = 5√0
Find the square root
(g . h)(0) = 5(0)
Find the product
(g . h)(0) = 0
Hence, the value is 0
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Here is a vertical algorithm that we can use to find 60.19 – 47.52.Which place value column(s) will require regrouping?Please see image below.
Answers
Regrouping happens when we need to "borrow" value from the higher order digits to perform a subtraction properly. This happens on the tenths, because we need to subtract 5 from 1, which we can't do normally. So we need to regroup from the ones and tens, in order to solve the problem. The correct answer is B.
Solve the equation for all complex and real solutions. Use potential zeros and synthetic division[tex]5x^4+7x^3+119x^2+175x-150=0[/tex]
Answers
Answer: the complex solutions are:
Step-by-step explanation: x = 5i , -5i , 3/5 ,-2
Larry and his brother wanted to put new carpet down in threerooms in his house. The three rooms measured 10' x 12, 13' x 15,and 12' x 12'. If the carpet Larry wants to use is $25.56 a sq. yd.and the roll of padding is $99 for a 30 sq.yd. roll, answer thefollowing questions. Remember that 1 square yard = 9 square feet.1. Total square footage to be covered with carpeting would besquare feet.2. How many square yards would that be?sq.yd.3. Based on the price of $25.56 a sq.yd., what would the total costbe for the carpeting? $4. To make sure Larry has enough padding, how many rolls wouldhe have to buy?What would that cost? $5. What would the total cost of the carpeting job be includingcarpet and padding? $
Answers
Find the area of each room and then add the three areas.
[tex]\begin{gathered} 10\times12=120 \\ 13\times15=195 \\ 12\times12=144 \\ \\ 120+195+144=459 \end{gathered}[/tex]The total square footage to be covered is 459.
Part 2)Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:
[tex]\frac{459}{9}=51[/tex]Then, the area is equal to 51 square yards.
Part 3)The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:
[tex]25.56\times51=1303.56[/tex]The total cost for the carpeting is $1303.56.
Part 4)Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is 2.
The cost for 2 rolls would be 2*$99 = $198.
Part 5)Add the cost of the two rolls of padding and the carpeting job to find the total cost:
[tex]\text{ \$}198+\text{ \$}1303.56=\text{ \$}1501.56[/tex]Then, the total cost of the carpeting job including the carpet and padding would be $1501.56.
Therefore, the answers are:
Part 1) 459 square feet.
Part 2) 51 square yards.
Part 3) $1303.56
Part 4) 2 rolls for $198
Part 5) $1501.56
Is tim correct? explain why or why not and provide three examples that prove whether or not tim’s statement is correct
Answers
Given:
[tex]\text{Tim has the expression x}^2[/tex]Yes, Tim is correct.
Expression is having the square so , wheather the input is negative or positive the output will always gives the positive values.
All real inputs will give the positive output.
Example:
[tex]\begin{gathered} (-2)^2=4 \\ (-1.1)^2=1.21 \\ 5^2=25 \end{gathered}[/tex]Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer
Answers
Given:
13th term = -60
33rd term = -160
Find:
14th, 15th, 16th, and 17th term
Solution:
For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:
[tex]\frac{a_{33}-a_{13}}{33-13}[/tex]Let's plug in the values of a₃₃ and a₁₃ in the formula above.
[tex]\frac{-160-(-60)}{33-13}[/tex]Then, solve.
[tex]\frac{-100}{20}=-5[/tex]Hence, the common difference between the terms is -5.
So, the next 4 terms after a₁₃ are shown below:
[tex]\begin{gathered} a_{14}=-65 \\ a_{15}=-70 \\ a_{16}=-75 \\ a_{17}=-80 \end{gathered}[/tex]
Hello, I need some assistance with this homework question please for precalculusHW Q30
Answers
EXPLANATION
Since the degree is 6, the polynomial has 6 zeros:
Then, using the Complex Root Theorem, since the polynomial has 2 complex roots, thus the conjugate of 5 + i is 5 - i, and the conjugate of 7 - i is 7 + i:
In conclusion, the remaining zeros are: 5 - i, 7 + i
I will show you the pic
Answers
The general form of a linear equation is given by:
y = kx
where k is a constant.
From the given options you can notice that the only equation similar to the previous one is:
y = 1/6 x
Then, the previous equation is the linear equation.
S
SOLUTION
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows
the relationship between the perimeter of an equilateral triangle and the
perimeter of a regular pentagon. What is the perimeter of the pentagon?
A 20
B 50
C 100
D 150
Nikia chose A as the correct answer. How might she have gotten that answer?
Answers
The perimeter of pentagon is 150 so option D is correct.
Given:
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.
3(3x-10) = 5(x+10)
9x - 30 = 5x + 50
9x - 5x = 30 + 50
4x = 80
divide by 4 on both sides
4x/4 = 80/4
x = 80/4
x = 20.
perimeter of pentagon = 5(x+10)
= 5(20+10)
= 5*30
= 150.
Therefore the perimeter of pentagon is 150 so option D is correct.
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if you could give me the answer without explantion i would be happy to leave a good review
Answers
The coordinates of the fourth side are (6, -8)
Explanation:Let the coordinate of the fourth side be (x, y)
The diagonals of a parallelogram bisect eachother, so the midpoint of (-3, -2) and (x, y) is equal to the midpoint of (4, -4) and (-1, -6)
[tex]\begin{gathered} (\frac{x-3}{2},\frac{y-2}{2})=(\frac{4-1}{2},\frac{-6-4}{2}) \\ \\ (\frac{x-3}{2},\frac{y-2}{2})=(\frac{3}{2},-5) \\ \\ \frac{x-3}{2}=\frac{3}{2}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ \\ \frac{y-2}{2}=-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \end{gathered}[/tex]Solving these equations:
x - 3 = 3
x = 3 + 3 = 6
and
y - 2 = -10
y = -10 + 2 = -8
The coordinates are (6, -8)
Can anyone answer this
Answers
Answer:
add the number of sides then divide the number by the number of sides
In the rectangle below, R V=3 x+8, S V=6 x-4, and m∠ V R S=54°. Find the value of x and m∠ V U R
Answers
From the information given about the above quadrilateral, that is, the rectangle x is equal to 4, and m∠VUR is equal to 36°.
What is a quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners in geometry. The name comes from the Latin words quadri, a variation of four, and latus, which means "side."
The results above are derived as follows:
To find x note that the diagonals of a triangle are congruent. This means that RT = SU.
⇒ 3x + 8 = 6x - 4 (add 4 to both sides)
3x + 8 + 4 = 6x - 4 + 4
3x + 12 = 6x (Collect like terms over the equation sign)
12 = 6x - 3x
12 = 3x (divide both sides by three)
x = 12/3
x = 4
To derive m∠VUR,
Recall the properties of a rectangle:
Opposites sides a parallelOpposite sides are equalAll internal angles measure 90°The diagonals of a rectangle are equal.Also, note that;
SRU = 90°
hence
∠VRU = ∠SRU - ∠VRS
that is:
∠VRU = 90 -54 = 36°
If ∠VRU = 36°, then
∠VUR = 36° [The diagonals of a rectangle are equal.]
Hence ΔRVU is an Isosceles triangle. Since this is true, and it is also true that the two angles opposite to the equal sides of an isosceles triangle are congruent to each other,
Then indeed, ∠VUR = 36°
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Find a point N on the segment with endpoints K(-2, -3) and L(4,3) that partitions thesegment, starting at point K, 1/3 of the way to point L.
Answers
First find the length of the segment KL
Apply the formula for distance between two points as;
d = √{y2-y1}^2 + {x2-x1}^2 where
y1= -3 , y2 = 3 , x1 = -2 and x2 = 4
d= √ {3--3}^2 + { 4--2}^2
d= √ 9^2 + 6^2
d= √ 81 + 12
d= √93 = 9.6
So the length of the segment is 9.6
From point K {-2, -3} , find 1/3 of the length to locate point L
This will be : 1/3 * 9.6 =3.2
This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}
d = √{y2-y1}^2 + {x2-x1}^2
3.2 = √{y--3}^2 + {x--2}^2
3.2 =√ {y+3}^2 +{x+2}^2
3.2^2 = {y+3}^2 + {x+2}^2
10.3 = y^2 + 6y + 9 + x^2 +4x +4
10.3 = y^2 + 6y +x^2 +4x +9+4
10.3 = y^2 + 6y +x^2 +4x +13
0=y^2 +6y +x^2 +4x +13-10.3
0= y^2 +6y +x^2 +4x +2.7
y^2 + 6y +x^2 +4x +2.7 = 0
{-0.9,-0.5)
What is the congruence correspondence, if any, that
will prove the given triangles congruent?
A) ASA
B)SAS
C) SSS
D) none
Answers
Answer:
A) ASA
Step-by-step explanation:
You want to know the relevant congruence postulate given the markings of angles and sides shown in the diagram.
MarkingsThe arc and hash marks show on the angles mean the angles with matching markings are congruent. Two angles are shown as congruent to their corresponding angles in the other triangle.
The hash mark on the sides mean the sides with matching markings are congruent. One side between the marked angles is shown as congruent to the corresponding side in the other triangle.
The letters A and S in the congruence postulate designations refer to corresponding Angles and Sides, respectively. So, two angles with a side between them would be identified as ASA.
The ASA congruence postulate applies.
Option A) ASA is the correct answer for the given triangle in the question. ASA is the congruence correspondence.
What is congruence correspondence?
Each triangle's vertices must match one another exactly. This expression signifies that each triangle's side and angle measurements match up with a side or angle of the other triangle. To have a one-to-one correspondence, triangles don't necessarily have to be congruent, but when they are, knowing the correspondence of the triangles is important to determine precisely which sides and which angles are congruent.
According to congruence postulate,
Angles with matching markings are congruent if an arc or hash mark appears on them. The relationship between two angles and the corresponding angles in the other triangle is demonstrated.
The hash marks on the sides indicate that the markings on the sides that match are consistent. The opposite triangle's equivalent side is shown to be congruent to the side between the highlighted angles.
The congruence postulate designations begin with the letters A and S, which stand for matching Angles and Sides, respectively. Therefore, ASA would be used to describe two angles with a side in between them.
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parallel linessolve for x
Answers
We have two parralel lines with angles 32x + 4 and 34x - 2
From the figure, the angles are corresponding angles
Corresponding angles are equal
That is,
34x - 2 = 32x + 4
Collect the like terms
34x - 32x = 4 + 2
2x = 6
Divide both sides by 2
2x / 2 = 6 / 2
x = 3
The answer is 3
how much bags of fertilizer will brett need to cover the entire garden.
Answers
Area A = ?
Bag area covers = 54 ft2
Square Area S = 18ft X 18 ft
. = 324 ft2
Then now divide S/B
S/B = 324/54
. = 36/6
. = 6
Then answer is
Brett will need 6 bags of fertilizer
Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cups of kool-aid. how 4many cups of sugar does she need to make 4 cups of kool aid. HELP PLS
Answers
Lily needs 3/2 cup of sugar to make 4 cups of kool-aid.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cup of kool-aid which is given in the question.
We have to determine the number of cups of sugar she needs to make 4 cups of kool-aid.
Let the number of cups of sugar would be x she needs to make 4 cups of kool-aid.
As per the given information, we can write the ratio as:
1/4 cup of sugar : 2/3 cup of kool-aid = x cup of sugar : 4 cup of kool-aid
⇒ 1/4 ÷ 2/3 = x ÷ 4
⇒ (1/4) / (2/3) = x / 4
⇒ (1/4) × (3/2) = x / 4
⇒ 3/8= x / 4
⇒ x = (3 × 4)/8
⇒ x = 12/8
⇒ x = 3/2
Therefore, she needs 3/2 cups of sugar to make 4 cups of kool-aid.
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Summary
Give an example of a proportional relationship and write an equation that represents the relationship.
Answers
The proportional relationship is represented by the formula, y = kx, which demonstrates that y increases at the same rate as x does
Relationships between two variables that are proportional occur when their ratios are equal.
Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.The ratio of the constant values of two proportional quantities is known as the proportionality constant.When either the ratio or product of two changing values results in a constant, that pair of values is said to be in proportion.The Direct Variation and Inverse Variation types of proportions between the two provided values determine the value of the proportionality constant.The direct proportionality formula, y = kx, demonstrates that y increases at the same rate as x does. The cost per item (y), which is inversely proportional to the number of things purchased (x), is represented by the symbol y x.By using the indirect proportionality formula, y = k/x, it can be seen that when y rises, x falls, and vice versa.Therefore the proportional relationship is represented by the formula,
y = kx .
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Round 0.4275 to the nearest thousand
Answers
we have
0.4275
if we round to the nearest thousand, we look at the third digit of our number
0.4275
do you know the answer now?
0.42 is not correct
and only 2 decimals will be rounded to the nearest hundreth
becuase we have a 5 after 7, the number will be rounded up
0.428
this is the answer
if we would have for example
0.3521
the rounded to the nearest thousand would be 0.352
please answer this using the foil method[tex] {9x}^{2} + 60x + 100[/tex]
Answers
Answer
Given expression
[tex]9x^2+60x+100[/tex]By factorization, we have
[tex]\begin{gathered} 9x^2+30x+30x+100 \\ 3x(3x+10)+10(3x+10) \\ (3x+10)(3x+10) \end{gathered}[/tex]Now to check, using FOIL method, we have
F = First, i.e 3x(3x) = 9x²
O = Outer = 3x(+10) = +30x
I = Inner = +10(3x) = +30x
L = Last = +10(+10) = +100
Solve for n in the proportion 7/3 = n/21.
Answers
7/3 = n/21
We need to find the value of n,
Cross multiplying,we get
3n = 21 x 7
=> 3n = 147
=> n = 147/3
=> n = 49 is the required answer
help me with geometry proof, pls I did really bad on this homework and I need help, This is what I hard:State. Just.segment AB ll DC; Given
Answers
Answer:
Triangle ABC is congruent to DCE by SAS Theorem.
Step-by-step explanation:
Since AB is parallel to DC, we can say that BC is congruent to CE and AC is congruent to DE, then:
If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangle is congruent.
Triangle ABC is congruent to DCE by SAS Theorem.