The value of k that will make the quadratic equation kx² - 4x + 1 = 0 to have two equal roots is; k = 4
What are the roots of the Quadratic Equation?The general form of representing a quadratic equation is;
ax² + bx + c = 0
Now, we are given the quadratic equation which is;
kx² - 4x + 1 = 0
Now, for a quadratic equation to have 2 equal roots, it means that;
b² = 4ac
Thus, applying that to our given quadratic equation gives us;
(-4)² = 4(k * 1)
4k = 16
k = 4
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2 Find x and y
130⁰ answer
Answer: x = 80°, y = 50°
Step-by-step explanation:
We have an isosceles triangle.
As you can see, 130° lies on a straight line. A straight line = 180°.
The base angles of an isosceles triangle are equal. This means 180° - 130° = y.
So, y = 50°.
The total measures of any triangle is 180 degrees.
The total measure for the base angles here 100 degrees. That is, 50° + 50° =
100°.
How do we find x?
x = 180° - 100
x = 80°
Find the value of x in degrees for which d//m
Answer:
x = 31
Step-by-step explanation:
87=2x-25
-25 on each side
62=2x
divide each side by 2
31=x
x=31
What is 21.00$ with a 7%
tax
Answer:
22.47
Step-by-step explanation:
7/100 = 0.07 (the tax rate) 21 * 0.07 = 22.47, the tax adds on 1.47
need help asap
please do it
It is to be noted that the information for the completed table is given accordingly to show the perimeters in millimeters and in centimeters.
What is a Perimeter?Perimeter simply refers to the total or sum of all the sides of a geometric shape. Note that the perimeter in units is obtained by counting the number of rectangles.
In the case of A:
Perimeter in Units = 10 Units.
Length is 60mm and width is 40mm
Perimeter = 30 + 20 + 30 + 20 = 100mm; and 10 cm
Recall that I cm = 10mm.
Hence, 100 /10 = 10 cm.
In the case of shape B:
Perimeter in Units = 41 Units.
Length is 400mm (that is 200 + 200)
Breath is 40mm (20 + 20)
Perimeter therefore is:
400 + 40 = 440mm
Perimeter in cm = 44
Recall, 10mm = 1cm
In the case of shape C:
Perimeter in Units = 36 Units.
Length is 10cm (that is 5 + 5)
Breath is 14mm (7 + 7)
Perimeter therefore is:
10+ 14 = 24cm
Perimeter in mm= 240
Recall, 10mm = 1cm
In the case of Shape D:
Perimeter in Units = 51 Units.
Length is 200mm (that is 100 + 100)
Breath is 100mm (50 + 50)
Perimeter therefore is:
200 + 100 = 300mm
Perimeter in cm= 230
Recall, 10mm = 1cm
In the case of Shape D:
Perimeter in Units = 53 Units.
Length is 260mm (that is 130 + 130)
Breath is 80mm (40 + 40)
Perimeter therefore is:
260 + 80 = 340mm
Perimeter in cm= 34
Recall, 10mm = 1cm
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A teacher is buying markers. Each set of markers includes 5 markers and cost $3.00. The teacher uses a $3-off coupon toward the total cost of all the markers bought. If there is no tax added to the final cost of the markers after the coupon and the teacher paid a total of $15, how many markers did she buy?
A. 6
B. 25
C. 30
D. 35
Answer:
30 markers
Step-by-step explanation:
(15 what she spent)+(3 the 3 dollors off)=
18/(3 the price of markers)=
(6 sets)*(5 how many is in a set)=
(30 final anwser)
20 points. Someone please help
Step-by-step explanation:
[tex](4(2) \: - 6(7) \: 5(1)) \\( 2( - 1) \: 4(5) \: - 1(2) ) \\ (8 \: - 42 \: \: 5 \\ - 2 \: \: \: 20 \: \: - 2)[/tex]
2 Please help Anyone
Equation of the first line = [tex]y=-\frac{1}{2} x+1[/tex]
Equation of the second line = [tex]y=-\frac{5}{2} x -1[/tex]
What is the equation of the first line?
Co-ordinates of the first line (x, y) = (-2,2), (0,1), (2,0), (4,-1)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{1-2}{0+2} \\\\=-\frac{1}{2}[/tex]
The slope -intercept form of a line is given by,
y = mx + b ---(1)
Let us substitute ( x, y )= (-2, 2) in (1)
2=(-1/2)*-2+b
2-1= b
b = 1 ----(2)
Let us substitute m and b in the slope-intercept equation (1)
[tex]y=-\frac{1}{2} x+1[/tex]
What is the equation of the second line?
Co-ordinates of the second line (x, y)=(-4,9), (-2,4), (0,-1), (2,-6)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{4-9}{-2+4} \\\\=-\frac{5}{2}[/tex]
The slope -intercept form of a line is given by,
y = mx + b ---(3)
Let us substitute ( x, y )= (-4, 9) in (1)
9 = (-5/2)*-4+b
2 - 1 = b
b = - 1 ----(4)
Let us substitute m and b in the slope-intercept equation (3)
[tex]y=-\frac{5}{2} x -1[/tex]
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help pls giving 20 points
Answer:
A
Step-by-step explanation:
On a number line, I would start at 32 and then go left on the number line 17 spaces. This would land me at positive 15.
The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?
By using a rotation rule, the image of point P = (- 4, 1) after rotating 180° counterclockwise using center (- 3, 0) is equal to point P'(x, y) = (- 2, 1).
How to determine the coordinates of the image of a point by using a transformation ruleIn this problem we find the case of a point that must be rotated 180° counterclockwise (+ 180°) about the point (- 3, 0). Rotation is a kind of rigid transformation, that is, a kind of transformation applied on a point such that Euclidean distance is conserved. The rotation formula for a point P(x, y) = (x, y) around the center O(x, y) = (Ox, Oy) is introduced below:
P'(x, y) = (Ox + (x - Ox) · cos θ - (y - Oy) · sin θ, Oy + (x - Ox) · sin θ + (y - Oy) · cos θ)
Where θ is the angle of rotation.
If we know that O(x, y) = (- 3, 0), P(x, y) = (- 4, 1) and θ = 180°, then the coordinates of the image are:
P'(x, y) = (- 3 + [- 4 - (- 3)] · cos 180° - (1 - 0) · sin 180°, 0 + [- 4 - (- 3)] · sin 180° + (1 - 0) · cos 180°)
P'(x, y) = (- 3 - [- 4 - (- 3)], - 1)
P'(x, y) = (- 3 - (- 1), - 1)
P'(x, y) = (- 2, - 1)
The coordinates of the image are P'(x, y) = (- 2, 1).
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i need help on this, thanks
Answer:
m<1 = 159° m<2 = 21° m<4 = 21°
Step-by-step explanation:
Since angle measure 3 was found, seeing that 3 and 1 are vertical angles (congruent) they equal the same, meaning angle measure 1 is also 159°. Also seeing that angle measure 3 and 2 are supplementary angles (2 or more angles that add up to 180°) subtracting 159° will give you 21°. Once again there are another set of verital angles, 2 and 4 making 4 also 21°
Factorise
y²-2y-48
Answer: y²-2y-48=(y-8)(y+6)
Step-by-step explanation:
[tex]y^2-2y-48=\\\\y^2-8y+6y-48=\\\\y(y-8)+6(y-8)=\\\\(y-8)(y+6)[/tex]
Answer:
y²-2y-48=(y-8)(y+6)
Step-by-step explanation:by factorization
y2-2y-48= y2-8y+6y48= y(y-8)+6(y-8)= (y-8)(y+6)
c. What is -3-6? What does that tell you about how many points Soledad has after the next round?
Step-by-step explanation:
i.)add 3 in 6 which = 9
ii.) follow the negative sign of the larger value which now ur finally answer is -9
if 4 years you shrink down for 1.7cm how much do you shink in year
Answer:
In a year you can shrink 0.625cm
Step-by-step explanation:
1.7/4=0.625
Use the given information determin which lines if any in the figure to the right of the parallel justify each conclusion with a theorem or postulate
Given <2 is supplementary to <3 Because it's given that to a supplementary to 3 lines ______ Are parallel by the ______
Angle 2 is supplementary to Angle 3 Because it's given that to a supplementary to 3 lines A and B are parallel by the transverse line.
What are supplementary angles?Two Angle whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
If ∠ 8 is supplementary to ∠ 9, then line x and y must be parallel lines wheres line s is the transverse line.
∠ 7 = ∠ 4.
Now, ∠ 7 = ∠ 2 and ∠ 4 = ∠ 9.
So, ∠ 2 = ∠ 3 {supplementary angles}
Angle 2 is supplementary to Angle 3 Because it's given that to a supplementary to 3 lines A and B are parallel by the transverse line.
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Please help, super behind in the class and still trying to learn and catch up.
Given the equation and table below, determine the following
(Picture below)
Answer: See attached and/or view below.
Step-by-step explanation:
Since we are given the equation, we can plug the values into it and solve for the unknown. We will solve by isolating the variable and using reverse operations.
x = 1, y = 34
2x + y = 36
2(1) + y = 36
2 + y = 36
y = 34
x = -2, y = 40
2x + y = 36
2(-2) + y = 36
-4 + y = 36
y = 40
y = 18, x = 9
2x + y = 36
2x + (18) = 36
2x = 18
x = 9
The equation y = 0.44x + 87 models the cost y of renting a car if the car is driven x miles.
According to the model, what is the best estimate of the cost for renting a car if you plan to drive 545 miles? Please round your answer to the nearest dollar.
7. Consider a line containing the points (0,14) and (2, -8). What is the slope of any line
perpendicular
to it?
Answer:
a= (0,14) (2,-8)
Step-by-step explanation:
Fae is following a recipe to make dough. The amount of water (in ounces) she uses depends on the amount of flour she uses (in cups). The amounts for each ingredient are shown in the graph.
The unit rate of ounces of water per cup of flour for this situation is; 3 ounces per cups
What is the unit rate of the graph?
From the given graph, we are expected to find the unit rate of ounces of water per cup of flour for the situation.
Now, to find the unit rate , all we need to do is to pick two coordinates on the line graph and find the slope. Thus;
Slope = (y2 - y1)/(x2 - x1)
Slope of graph = (12 - 9)/(4 - 3)
Slope = 3/1
Slope = 3
Let us pick another two points to verify;
Slope = (6 - 3)/(2 - 1)
Slope = 3/1
Slope = 3
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When Sam launched a potato from their potato cannon the potato traveled a horizontal distance of 150 feet and, at its highest, reached 90 feet.
Part A. Create a graph to represent the scenario. The graph should include at least the x- and y-intercepts and the vertex. (A complete graph consists of axis labels and appropriate scales, ordered pairs for each identified point, the function, and appropriate domain/range.)
Part B. Write a function to model the scenario.
Part C. Create a table of values to represent the scenario. Be sure to include at least five
values. Values should include at least the x- and y-intercepts and the vertex.
Part D. Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation.
(PLEASE HELP)
This statement about distance is proved.
What is distance ?
It is length of space between two points.
Okay, so the first three components of this issue involve more physics and math. So, part A received the formula Ds = R. D. Data. We have to track down S. Therefore, we simply integrate both sides equally using R. D. Data. Our data are provided. Therefore, the upon integration over our data is just R 0 Santa plus 12 beta zeta squared for part B. We'll make sure S = V T. We combine these two by using the above equation as an equal. In order to allow it to reach its roots once positive, we can see that this is Justin's equation for data. The other negative, which is naturally a positive one because it has the proper physical meaning, would indicate that the rotation is occurring in the opposite direction.
Standard units, uh, are zero point 24/7 times, so switch to the nature radio's negative six setting. Additionally, we are given the time, which is 74 minutes, or 4440 seconds. Thus, plugging everything. Injecting R 0 and data mm hmm into the expression for data. Therefore, we enter better Data. V also appears. Everything is therefore known. We can confidently conclude that the data is, um, 1.337 x 10-5 brilliant. or 2.13 x 10 to 4 revolutions, in terms of turns. Okay. We simply re-insert the numbers for beta and tr zero V into the previous expressions for omega and alpha in the final section of the problem.
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An artist uses a coordinate plan to create a design. As part of the design, the artist wants to Graph the point ( - 6.5, 2). How should the artist graph this point.
6.5 units to the left of the origin, and 2 units above the origin
What is coordinate plane ?A coordinate plane is a surface with two dimensions made up of two number lines. It is created when the origin, the point at which the X-axis and Y-axis cross, is reached. To locate points, one uses the numbers on a coordinate grid. A coordinate plane is useful for graphing points, lines, and many other things. It serves as a map and provides clear instructions for getting from one place to another
What are coordinates ?Coordinates are a pair of numbers that identify a specific point on a coordinate plane, often known as a grid of coordinates. The ordered pair (x, y), which corresponds to the X-coordinate and the Y-coordinate, is expressed in parenthesis and is used to identify a point in a coordinate plane. Depending on where the point is in relation to the different quadrants, these coordinates may be positive, zero, or negative.
6.5 units to the left of the origin, and 2 units above the origin
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You must cut a triangle out of a sheet of paper. The only
requirements you must follow are that one of the angles
must be 60°, the side opposite the 60° angle must be 40
centimeters and one of the other sides must be 15
centimeters. How many different triangles can you make?
1,2,3 or4?
Estimate 0.046138792 to the nearest hundredth. Express your answer as a single digit time power of ten.
The value of 0.046138792 estimated to the nearest hundredth is 0.05 and can be expressed in the form [tex]5*10^{-2}[/tex].
This is a question of place values.
Given number:-
0.046138792
We have to estimate the given number to the nearest hundredth. Also, we have to express the answer as a single digit to power of ten.
In the given number, we can see that,
After decimal,
tenth digit is 0
hundredth digit is 4
thousandth digit is 6
and so on.
We have to limit our answer till hundredth digit.
As thousandth digit is 6 we will estimate the number as 0.05.
Now,
0.05 = 5/100
= [tex]\frac{5}{10^2} = 5*10^{-2}[/tex]
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in the graph below find the coordinates of the image point O is the origin and P is the point (1,-2) Ry and Rx are Reflections around the X & Y axis
If (1, -2) is reflected over the x-axis, then the image is (1, -(-2)) = (1, 2).
If (1, -2) is reflected over the y-axis, then the image is (-1, -2).
Then, the points are image over the x-axis is (1, 2), and the image over the y-axis is (-1,-2).
what makes this statement true?
-1/8 ? -3/8
Answer:
-1/8>-3/8
Step-by-step explanation:
You can write it as a decimal.
-0.125 ? -0.375
pls help me on this one i need them quick
The slope of the line is that passing through the points (-1,-3) and (1,3) is m = 2
From the graph, we have to find the two points to find the slope of the line
The two points are (-1,-3) and (1,1)
The slope of the line m = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
Where m is the slope of the line
[tex](x_{1} ,y_{1})[/tex] are the coordinates of first point
[tex](x_{2} ,y_{2})[/tex] are the coordinates of second point
substitute the values in the equation of slope of the line
The slope of the line m =[tex]\frac{1-(-3)}{1-(-1)}[/tex]
= 4/2
= 2
Hence, the slope of the line is that passing through the points (-1,-3) and (1,3) is m = 2
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Write a linear equation of a slope intercept form for a line that passes through the point (-2, 9) and has a slope of:-5/2
Answer:
[tex]y = - \frac{5}{2} x + 4[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y= mx +c, where m is the slope and c is the y-intercept.
Start with the slope when forming the equation.
Given that the slope is [tex] - \frac{5}{2} [/tex], [tex]m = - \frac{5}{2} [/tex].
Substitute the value of m into the equation:
[tex]y = - \frac{5}{2} x + c[/tex]
The value of c can be found by substituting a pair of coordinates that the line passes through.
When x= -2, y= 9,
[tex]9 = - \frac{5}{2} ( - 2) + c[/tex]
9= 5 +c
c= 9 -5
c= 4
Thus, the equation of the line is [tex]\bf{y = - \frac{5}{2} x + 4}[/tex].
Additional:
What is a linear equation?
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Answer in graph form. Find 0 if cos0= 4/7 and sin0 is negative
The θ lies in the 4th quadrant of the graph.
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.The coordinate plane system's four quarters are referred to as quadrants. A quadrant is the name of one of the four divisions. A quadrant, or sector of 90 degrees, is the term used to describe a circle's quarter.In the question, Cosθ = 4/7 and Sinθ is negative.Cosθ is positive in the 1st and 4th quadrants.Sinθ is negative in the 3rd and 4th quadrants.Thus, θ lies in the 4th quadrant of the graph.To learn more about quadrants, visit :
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12 = 5w - w solve for w
Answer:
w = 3
Step-by-step explanation:
12 = 5w - w = 4w ( divide both sides by 4 )
3 = w
Answer:
w=2.4
Step-by-step explanation:
12 = 5w
Divide both sides by 5.
12/5=2.4
5/5=w
2.4=w
Brayden deposited $2700 into a savings account that has an annual simple interest rate of 0.3%. find the amount in the savings account after each number of years.
The principal plus interest which gives the amount in the account after each year are;
First year, $2,708.7Second year, $2,717.4Third year, $2,726.1Fourth year, $2,734.8Fifth year, $2,743.5What is a simple interest applied to an amount?Simple interest is the product of the principal amount, the rate and the time of investment
The amount Brayden deposited in the savings account, P= $2,700
The interest on savings account, R = 0.3% simple interest
The simple interest formula is, I = P•R•T
The interest in the account after each year is therefore;
1st year = $2,700×0.3%×1 = $8.7
The interest in 2 years, I = 2×$8.7 = $17.4
3 years, I = $8.7 × 3 = $26.1
4 years, I = $8.7 × 4 = $34.8
5 years, I = $8.7 × 5 = $43.5
The amount in the account after each of the 5 years are therefore;
1st year, A = $2,700 + $8.7 = $2,708.7
2nd year, A = $2,700 + $17.4 = $2,717.4
3rd year, A = $2,700 + $26.1 = $2,726.1
4th year, A = $2,700 + $34.8 = $2,734.8
5th year, A = $2,700 + $43.5 = $2,743.5
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The points ( – 5,j) and (5, – 6) fall on a line with a slope of – 7/10 . What is the value of j?
Answer:
j = 1
Step-by-step explanation:
calculate the slope m between the 2 points and equate to - [tex]\frac{7}{10}[/tex]
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, j ) and (x₂, y₂ ) = (5, - 6 )
m = [tex]\frac{-6-j}{5-(-5)}[/tex] = [tex]\frac{-6-j}{5+5}[/tex] = [tex]\frac{-6-j}{10}[/tex]
then equating gives
[tex]\frac{-6-j}{10}[/tex] = - [tex]\frac{7}{10}[/tex] ( cross- multiply )
10(- 6 - j) = - 70 ( divide both sides by 10 )
- 6 - j = - 7 ( add 6 to both sides )
- j = - 1 ( multiply both sides by - 1 )
j = 1