The equation of line in point slope form is y = -3x -4
Given,
The points which the line passes through;
(x, y) = (-3,5)
Slope, m = -3
We have to find the equation in point slope form;
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
Point slope form;
y - y₁ = m(x - x₁)
Then,
y - 5 = -3(x - -3)
y - 5 = -3x -9
y = -3x - 9 + 5
y = -3x - 4
That is,
The equation of line in point slope form is y = -3x -4
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Solve two and one-third times four-fifths equals blank.
four-sixths
one and twelve-fifteenths
one and thirteen-fifteenths
four and four-sixths
The solution to the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.
The correct answer option is option C
How to solve the product of a fraction?A fraction refers to a part of a whole, especially a comparatively small part. It is also the ratio of two numbers, the numerator and the denominator, usually written as one above the other and separated by a horizontal bar.
A numerator is the number above the horizontal bar while the denominator is the number below the horizontal bar in a fraction.
Two and one-third times four-fifths
= 2 1/3 × 4/5
= 7/3 × 4/5
= (7 × 4) / (3 × 5)
= 28 / 15
= 1 13/15
Therefore, the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.
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Which expression is equivalent to the fraction below?
2/5
A. 2.2
B. 5.5
C. 5.2
D. 2.5
E. 2+5
F. 2 ÷ 5
Answer:F
Step-by-step explanation:
2/5=2 ÷ 5=0.4
y=x-7
5x+2y = 7
Use the substitution method.
O (0, -7)
O (-1, -8)
O (7,0)
O (3, 4)
-
Answer:
(3, -4)
Step-by-step explanation:
To solve the system of equations by substitution, start by labelling the 2 given information.
y = x - 7 -----(1)
5x + 2y = 7 -----(2)
Substitute (1) into (2):
5x + 2(x - 7) = 7
Expand:
5x + 2x - 14= 7
7x = 14 + 7
7x = 21
Divide both sides by 7:
x = 21 ÷ 7
x = 3
Substitute into (1):
y = 3 - 7
y = -4
Thus, the solution to the equations is (3 , -4).
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If it takes someone t minutes to drive run or walk a mile then their averages speed
EXPLANATION
Since the average speed is given by the equation:
[tex]s(t)\text{ = }\frac{60}{t}[/tex]Computing s(10) and s(12):
[tex]s(10)\text{ = }\frac{60}{10}=6[/tex]Now, computing s(12):
[tex]s(12)=\frac{60}{12}=5[/tex]In conclusion, the solutions are:
s(10) = 6 miles per hour
s(12) = 7 miles per hour
Match the pair of points with the slope of the line that joins them. (4,7) and (6,2)
We need to find the equation of the line that joins the points ( 4 , 7 ) and ( 6 , 2 )
The general equation of the line is ;
[tex]y=m\cdot x+b[/tex]where m is the slope and b is y - intercept
the slope = Rise/Run
Rise = 7 - 2 = 5
Run = 4 - 6 = -2
so, the slope :
[tex]m=\frac{5}{-2}=-2.5[/tex]So, the equation of the line :
[tex]y=-\text{2}.5x+b[/tex]Using any point from the given points to find the value of b
So, using ( 4 , 7 )
when x = 4 , y = 7
[tex]\begin{gathered} 7=-2.5\cdot4+b \\ 7=-10+b \\ b=7+10 \\ b=17 \end{gathered}[/tex]So, the equation of the line is:
[tex]y=-2.5x+17[/tex]A liniar equation has no solutions when the equation makes a false statement
Answer:
True
Step-by-step explanation:
Which of the following is the equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5?
The equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is; (x - 1)²/25 + (y + 3)²/49 = 1
What is the equation of the ellipse?The general format for equation of an ellipse with center (h, k) and vertical major axis is;
(x - h)²/b² + (y - k)²/a² = 1
We are given the following;
center at (1, -3)
a = 7
b = 5
Thus;
Equation of ellipse with given parameters is;
(x - 1)²/5² + (y + 3)²/7² = 1
This simplifies to;
(x - 1)²/25 + (y + 3)²/49 = 1
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What is the answer to this problem?
Answer:
see explanation
Step-by-step explanation:
solving the inequality
3 ≤ 4x - 13 ≤ 7 ( add 13 to each interval )
16 ≤ 4x ≤ 20 ( divide each interval by 4 )
4 ≤ x ≤ 5
the solution lies between 4 and 5 and can be equal to 4 and 5
this is indicated on Graph A
3.13 Which triangle congruence postulate or theorem proves that these triangles are congruent?
The triangle congruence postulate which proves that these triangle are congruent is SAS (Side Angle Side).
According to the SAS Postulate,
Two triangles are said to be congruent if their two sides and included angles are identical to those of another triangle's two sides and included angle.
According to the figures of the triangles, we can see
AC = XZ (Side)
∠ACB = ∠XZY (Angle)
BC = YZ (Side)
Hence, ΔABC ≅ ΔXYZ by SAS postulate.
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Which sum or difference is modeled by the algebra tiles?-1OA (x2 - 2x + 3) - (-x2 - 4x - 2) = 2x - 1OB. (x2 - 2x - 3) + (x2 - 4x + 2) = 2x - 1OC. 02 - 2x - 3) - (x2 + 4x + 2) = 2x - 1OD. (x2 - 2x-3) + (-x2 + 4x + 2) = 2x - 1© 2021 Edmentum. All rights reserved.
Okay, here we have this:
We will take as the first term the upper squares and as the second term the lower ones, and we obtain that:
[tex]\begin{gathered} (x^2-x-x-1-1-1)+(-x^2+x+x+x+x+1+1) \\ =(x^2-2x-3)+(-x^2+4x+2) \\ =2x-1 \end{gathered}[/tex]Here we obtain that the correct answer is the option D.
Two ships leaving the same marina at the same timeare 3.2 miles apart after sailing 2.5 hours. If theycontinue at the same rate and direction, how farapart will they be 2 hours later?2.56 miles3.52 miles5.76 miles6.08 miles
To answer this question, we need to take into account that the two ships continue sailing at the same rate and direction, and we can solve this using the unit rate concept, as follows:
[tex]\frac{3.2}{2.5}\frac{miles}{h}=1.28\frac{miles}{h}[/tex]If they continue sailing at this same rate, then, after two hours they will be:
[tex]1.28\frac{miles}{h}\cdot2h=2.56miles[/tex]They will have 2.56 miles more distance between them.
Then, they will be separated by a distance of:
[tex]3.2\text{miles}+2.56\text{miles}=5.76\text{miles}[/tex]In summary, we have that the answer is 5.76 miles.
8 squares and 10 triangles. What is the simplest ratio
The ratio for 8 squares and 10 triangles is 4:5.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, the ratio for 8 squares and 10 triangles will be:
= Number of square / Number of triangle
= 8/10
= 4/5
The ratio is 4:5.
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i need help on this math assignment
Answer: 3rd one is correct
Step-by-step explanation: got it right on the test
Maria spends $22 dollars on lottery tickets every week. shen also spends $133 per month on food. On an (annual) basis ,the money spent on lottery tickets is what percent of the money spent to buy food?
Maria spends $22 on lottery tickets every week and $133 every month on food yearly
This means that in a year
there are 52 weeks and she spends 22 x 52 = $1,144 on Lottery tickets
and there are 12 months in a year, so she spends 133 x 12 = $1,596 on food
The money spent to buy lottery tickets in relation to the money spent on food yearly in percentage is
[tex]\begin{gathered} \frac{1144}{1596}\times100 \\ =71.68\text{ percent approximately} \end{gathered}[/tex]What conjecture can you make about the sum of the frst 25 positive even numbers?Make a conjecture. Choose the correct answer below.O A. The sum is equal to the number of terms squared.OB. The sum is the product of the number of terms and the number of terms plus one.O C. The sum is the product of the number of terms and twoOD. The sum is the product of the number of terms and the number of terms minus one.
Given:
2+4+6+8+10+.....+50
[tex]2+4+6+10+\cdots+50=2(1+2+3+\cdots+25)[/tex]Let the sum of the first n natural numbers be
[tex]S_n=\frac{n(n+1)}{2}[/tex]Therefore the sum of first 25 positive even numbers is
[tex]2S_n=\frac{2n(n+1)}{2}[/tex][tex]2S_n=n(n+1)[/tex]Therefore,The sum is the product of the number of terms and the number of terms plus one.
Option B is the correct answer.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
154= -4(8+6r)+24r I want to know the answer
The equation 154 = -4(8+6r) + 24r has no solution because the variable becomes 0.
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We have to find the variable r of the equation to solve the equation.
A variable is a number represented with letters in an equation.
Therefore, let's find the variable r in the equation.
154 = -4(8+6r) + 24r
open the brackets on the right side of the equation
154 = - 32 - 24r + 24r
154 = -32 + 0
Therefore, the equation cannot be solved.
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Harold filled his swimming pool over the weekend. The pool has a capacity of 540 gallons. Harold put in 180 gallons of water on Saturday. The garden hose that Harold used supplies 9 gallons of water per minute. How long did it take for Harold to fill the pool to capacity on Sunday? Define a variable for the unknown quantity. Write and solve an equation to answer the question.
Pool Capacity = 540 gallons
Saturday = 180 gallons
Hose water rate = 9 gallons per minute
540 = 180+9m
Where m is the number of minutes (independent variable)
Solve for m :
540-180 = 9m
360 = 9m
360/9= m
40 =m
It will take 40 minutes.
Autumn has 55 cups of yogurt to make smoothies. Each smoothie uses 1/3
cup of yogurt. How many smoothies can Autumn make with the yogurt?
The total number of smoothies that Autumn can make with the yoghurt is 165.
We know that the total number of cups of yoghurt that Autumn needs to make smoothies is 55. Each smoothie uses 1/3 cup of yogurt. We need to calculate the total number of smoothies that Autumn can make with the yogurt.
Let the total number of smoothies be represented by the variable "N''. We will use the unitary method. The total number of smoothies that can be made is the ratio of the total number of cups of yoghurt to the fraction of a cup used to make one smoothie.
N = 55/(1/3)
N = 55*3
N = 165
Hence, Autumn can make 165 smoothies from 55 cups of yogurt.
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A ski resort rents snowshoes in the winter. the resort charges $1 per day and a flat fee of $3 to cover cleaning. write an equation that shows how the cost y, depends on the length of the rental in the day, x.
Answer:
3+ 1x = y
Step-by-step explanation:
a flat rebate means no matter how many days it will only be $3 so you add the 3 and you don’t know how many day you’ll rent the shoes so you put a variable next to the 1 and the 1 times however many days plus 3 will be your cost
Which of the following values are in the domain of the function graphed below? Check all that apply. A. -4 B. -1 C. 4D. 0E. 5 F. -2
Checking the given graph, it can be seen that the range of values of x is
[tex]\begin{gathered} rangeofvaluesofx, \\ -2\leq x\leq4 \end{gathered}[/tex][tex]undefined[/tex]The range of values of x are the values of the domain of the graph function
A. -4; -4 does not satisfy the function of the graph
Find the value of X express each answer as a decimal rounded to the nearest 10th
x = 11.1
Explanations:Note that the Pythagora's theorem is applied in solving this exercise
The Pythagora's theorem states that "the square of the hypotenuse equals the sum of the squares of the other two sides"
Hypotenuse is the longest side of the right-angled triangle:
Hypotenuse = 22
[tex]\begin{gathered} 22^2=19^2+x^2 \\ 484\text{ = }361+x^2 \\ x^2\text{ = 484 - 361} \\ x^2\text{ = }123 \\ x\text{ = }\sqrt[]{123} \\ x\text{ = }11.1 \end{gathered}[/tex]A box contains four tiles numbered 1,4,5 and 8 as shown . Kelly randomly chooses one tile , places it back in the box, then choose a second tile. what is the probability that the sum of two chosen tiles is greater than 7? A. 1/4 B. 5/16 C. 2/3 D. 11/16
Since Kelly chooses one tile, places it back in the box, and then choose another tile, we have that the total outcomes are 4x4 = 16.
Now, we can write easily all the outcomes :
[tex]\begin{gathered} \Omega=\mleft\lbrace(1,1\mright),(4,1),(5,1),(8,1), \\ (1,4),(4,4),(5,4),(8,4), \\ (1,5),(4,5),(5,5),(8,5), \\ (1,8),(4,8),(5,8),(8,8)\} \end{gathered}[/tex]notice that on the first row, only the event (8,1) gives us that the sum is greater than 7.
On the second row,we have the same for events (4,4),(5,4) and (8,4)
On the third row only (1,5) gives us a sum lesser than 7, then here we have 3 more events that fit our criteria.
On the last row, all events gives us a sum greater than 7,then we have another 4 events.
Then, the probability that the sum of two chosen tiles is greater than 7 is:
[tex]\frac{1}{16}+\frac{3}{16}+\frac{3}{16}+\frac{4}{16}=\frac{11}{16}[/tex]Need some help with this question I’ve been stuck on it for a bit
Answer: L BOZO
Step-by-step explanation:
L+RATIO=BOZO
A bucket of green paint 6 teaspoons of blue in it and 8 teaspoons of yellow paint to make a shade of green paint using 18 teaspoons of blue paint how many teaspoons of yellow
Answer:
24 teaspoons of yellow
Step-by-step explanation:
The ratio of blue to yellow is 6 to 8.
[tex] \frac{6}{8} = \frac{18}{y} [/tex]
We see that y = 24 since 18 = 3 × 6 and
24 = 3 × 8.
Avenger uses 9.4 pints of white paint and blue paint to paint her bedroom walls 4/5 of this amount is white paint in the breast is blue paint how many pints of blue paint did you use to paint her bedroom walls
Avenger uses 9.4 pints of white paint and blue paint to paint her bedroom walls 4/5 of this amount is white paint in the breast is blue paint how many pints of blue paint did you use to paint her bedroom walls
Let
x ----> pints of blue paint
y ----> pints of white paint
we have
x+y=9.4 -----> equation A
y=(4/5)*9.4
y=7.52
Find the value of x
x=9.4-y
x=9.4-7.52
x=1.88
therefore
answer is
1.88 pints of blue paintHow many solutions does this equation have?
4v = -6 + 5v
no solution
one solution
infinitely many solutions
Submit
4
Answer:
One Solution
Step-by-step explanation:
v can only equal 6
Select the transformations of g(x) = |1-2x+6| in relation to the parent function. HURRY PLEASE!!!
Answer:
Translated right [tex]\frac{7}{2}[/tex] units and vertical stretch
OR
translated right 3.5 units and vertical stretch
bcz
[tex]\frac{7}{2} =3.5[/tex]
Step-by-step explanation:
The absolute function is given as:
[tex]g(x) = |1-2x+6|[/tex]
If we simplify the equation, then we have
[tex]g(x) = |1-2x+6|\\g(x)=|-2x+6+1|\\g(x)=|-2x+7|\\g(x)=2|x-\frac{7}{2} |[/tex]
Now we can say that the transformation of g(x) to the parent function will be translated right [tex]\frac{7}{2}[/tex] units and vertical stretch (bcz you have a number (2) multiplying the function).
If the sign of the number that adds to the independent variable is negative, the transformation will be translated to the right, and if it is positive, it will be translated to the left.
what is the constant term of p(x)=(x+3)(x+2)(x+1)?
(PAHELP PLEASE)
Answer:
constant term = 6
Step-by-step explanation:
if you multiply the constant terms within each factor together you get the constant term of the expansion of p(x) , that is
constant term = 3 × 2 × 1 = 6
The graph of FX), shown below, has the same shape as the graph ofG(X) = x2, but it is shifted to the left 3 units. What is its equation?FX) ----A. F(x) = x² + 3B. FX) = (x - 3)2C. FX) = x2.3D. Rx) = (x + 3)?
We can represent the horizontal shift of a quadratic equation by adding or subtracting the constant h to the function
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ \text{where} \\ h\text{ is the horizontal shift} \end{gathered}[/tex][tex]\begin{gathered} \text{The function }f(x)\text{ has a default values of} \\ a=1 \\ h=0 \\ k=0 \\ \\ \text{A shift to the left of 3 units means that we will have }h=-3\text{ that means} \\ \\ F(x)=(x-(-3))^2 \\ \\ \text{Simplify},\text{ and we get} \\ F(x)=(x+3)^2 \end{gathered}[/tex]