Answers
Answer:
13. Two real solutions.
14. No real solutions.
Step-by-step explanation:
Given quadratic equations:
13. [tex]x^2+7x+10=0[/tex]
14. [tex]4x^2-3x+4=0[/tex]
[tex]{\large \textsf{Quadratic Formula: }} x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
What is the discriminant?
The discriminant (Δ) is b² - 4ac, which is under the square root in the quadratic formula. It is used to determine the number of real solutions (roots) of a quadratic:
When b² - 4ac > 0, the quadratic has two real solutions.When b² - 4ac = 0, the quadratic has one real solution.When b² - 4ac < 0, the quadratic has no real (complex) solutions.13. x² + 7x + 10 = 0
[tex]\implies a=\textsf{1},b=\textsf{7},c=\textsf{10}[/tex]
Find the discriminant value.
[tex]\implies \Delta = b^2 - 4ac[/tex]
[tex]\implies \Delta=(7)^2 - 4(1)(10)[/tex]
[tex]\implies \Delta=49 - 40[/tex]
[tex]\implies \Delta=9[/tex]
As [tex]9[/tex] > 0, this quadratic has two real solutions.
14. 4x² - 3x + 4 = 0
[tex]\implies a=\textsf{4},b=\textsf{-3},c=\textsf{4}[/tex]
Find the discriminant value.
[tex]\implies \Delta = b^2 - 4ac[/tex]
[tex]\implies \Delta = (-3)^2 - 4(4)(4)[/tex]
[tex]\implies \Delta = 9 - 64[/tex]
[tex]\implies \Delta = -55[/tex]
As [tex]-55[/tex] < 0, this quadratic has no real solutions.
Learn more about quadratic equations here:
brainly.com/question/28063094
brainly.com/question/27638369
Related Questions
Select the correct answer.
Consider this expression.
x-4
2(x+4)
For which product or quotient is this expression the simplest form?
O A.
B.
O C.
O D.
2x+8
x²16
x²16
2x+8
2x+8
x²16
x²16
2x+8
÷
÷
.
.
x² + 8x + 16
x +4
x +4
x² + 8x + 16
x² + 8x + 16
x + 4
x+4
x² + 8x + 16
Answers
The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Multiplying rational expressionsRational expressions are written in the form a/b where a and b are integers.
According to the question, we need to determine the expression that is equal to x-4/2(x+4)
From the fourth option;
x²-16/2x+8 * x+4/x²+8x+16
Factorize the quadratic part to have;
x²-16/2x+8 * x²+8x+16/x+4
(x+4)(x-4)/2(x+4) * x+4/(x+4)^2
Cancel out the common expression to have;
x-4 * 1/2(x+4)
x-4/2(x+4)
Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Learn more rational expression here: https://brainly.com/question/25292194
#SPJ1
In the diagram below, EF || HG, EF = 5, HG = 12, FI = 1 4x + 3
and HI= 6.1x - 6.5.
What is the length of HI?
Answers
The length of HI in the similar triangles is: (4) 24.
What are Similar Triangles?The corresponding sides of triangles that are similar to each other have ratios that are equal to each other, thus, they are proportional.
Triangle EFI and triangle GHI are similar to each other. Therefore, their corresponding sides have ratios that are equal. Thus, we will have the following:
HI/FI = HG/EF
Given:
EF = 5,
HG = 12,
FI = 1.4x + 3
HI = 6.1x - 6.5
Plug in the values
6.1x - 6.5/1.4x + 3 = 12/5
Cross multiply
5(6.1x - 6.5) = 12(1.4x + 3)
Open the bracket
30.5x - 32.5 = 16.8x + 36
30.5x - 16.8x = 32.5 + 36
13.7x = 68.5
Divide both sides by 13/7
13.7x/13.7 = 68.5/13.7
x = 5
HI = 6.1x - 6.5
Plug in the value of x
HI = 6.1(5) - 6.5
HI = 30.5 - 6.5
HI = 24
The length of HI in the similar triangles is: (4) 24.
Learn more about similar triangles on:
https://brainly.com/question/2644832
#SPJ1
use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi, that is equivalent to 17pi/6. with detailed steps pleasee
Answers
The equivalent angle in the interval [0, 2pi] is 5pi/6.
How to find the equivalent angle?
Remember that for any given angle θ in radians, we define a family coterminal or equivalent angles as:
A = θ + n*(2pi)
Where n is a whole number.
Now we want to find an angle equivalent to 17pi/6 that is on the range between 0 and 2pi.
Then we can write:
A = 17pi/6 + n*(2pi)
If we use n = -1, then we get:
A = 17pi/6 - 2pi = 17pi/6 - 12pi/6 = 5pi/6
This is the equivalent angle in the desired range.
If you want to learn more about equivalent angles:
https://brainly.com/question/24839702
#SPJ1
Find the Perimeter of the figure below, composed of a parallelogram and one
semicircle. Rounded to the nearest tenths place
4
14
Answers
The perimeter of the figure to the nearest tenth is 44.6 units
Perimeter of a figure?The perimeter of a figure is the sum of the whole sides.
Therefore,
A parallelogram has opposite sides equal to each other.
Therefore, the perimeter of the figure is as follows;
The figure combines a parallelogram and a semi circle.
Therefore,
perimeter of the figure = 4 + 14 + 14 + πr
perimeter of the figure = 32 + 3.14 × 4
perimeter of the figure = 32 + 12.56
perimeter of the figure = 44.56
perimeter of the figure ≈ 44.6 units
learn more on perimeter here: https://brainly.com/question/22532312
#SPJ1
Coplanar circles that have the same center, but not necessarily the congruent radii are called?
Answers
Coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
How to complete the blank?From the question, we have the following statements:
The circles are coplanar i.e. they are on the same planeThey have the same circleThe radii of the circles are differentAs a general rule, circles that have the above features are referred to as concentric circles.
This is so because concentric circles have the same center, and they do not intersect
Hence, coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
Read more about concentric circles at
https://brainly.com/question/960547
#SPJ1
1. Ellie has 2/8 pound of cheese. She used 1/2 of the cheese to make tacos. Since there are 16 ounces in one pound, how many ounces of cheese does Ellie use to make tacos?
Answers
The ounces of cheese Ellie uses to make tacos is 2
What is a unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Calculation :
1 pound = 16 ounces
Total cheese Ellie has = [tex]\frac{2}{8}[/tex] pound
Cheese required to make tacos = [tex]\frac{2}{8}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex] pounds
Ounces of cheese required to make cheese are [tex]\frac{1}{8}[/tex] × 16 = 2 ounces
learn more about the unitary method here :
brainly.com/question/17110989
#SPJ1
If you are choosing a single card from a standard deck of playing cards, what is
the probability that you draw a face card or a heart?
Your answer should be in the form of a fraction. Type it like this: 15/52.
Just to review:
• There are 52 cards in a deck.
• There are 4 suits with 13 cards each.
o 2 red suits - hearts and diamonds
o 2 black suites - clubs (look like clovers) and spades
• Each suit has an Ace, numbered cards 2-10, and 3 "face" cards--a Jack, Queen, and King.
Answers
Step-by-step explanation:
there are 4 suit with 13 cards each
A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. the apothem of the hexagon is 2 centimeters. a cylinder is cut out of the middle of a hexagonal prism. the hexagon has an apothem with a length of 2 centimeters and base side lengths of 2.3 centimeters. the prism has a height of 2 centimeters. the cylinder has a diameter of 1.6 centimeters. the equation for the area of a regular hexagon = one-half (apothem) (perimeter). what is the volume of metal in the hex nut, to the nearest tenth? use 3.14 for π.
Answers
Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists [tex]$$23.6 cm^3[/tex]
How to estimate the volume of metal in the hex nut?Diameter of the cylinder be d = 1.6 cm
Apothem of the hexagon be a = 2 cm
Thickness of the steel hex nut be t = 2 cm
Volume of the prism be [tex]V_p[/tex]
Volume of the cylinder be [tex]V_c[/tex]
Volume of metal in the hex nut,
[tex]$$V = V_p - V_c[/tex]
To estimate the volume of a prism,
[tex]$$V_p = A_b h[/tex]
Ab = n L a / 2
Number of the sides, n = 6
The side of the hexagon be L
Height of the prism, h = t = 2 cm
Central angle in the hexagon, A = 360°/n
A = 360°/6 = 60°
[tex]$tan (\frac{A}{2} )=(\frac{L/2}{a})[/tex]
simplifying the value of L, we get
[tex]$tan (\frac{60}{2} )=(\frac{L/2}{2})[/tex]
[tex]$tan 30}=(\frac{L/2}{2})[/tex]
[tex]$tan (\frac{\sqrt{3}}{3} )=(\frac{L/2}{2})[/tex]
Solving for L/2:
[tex]$\frac{2 \sqrt{3}}{3} =\frac{L}{2}[/tex]
Solving the value of L, we get
[tex]$2\frac{2 \sqrt{3}}{3} =L[/tex]
[tex]$\frac{4 \sqrt{3}}{3} =L[/tex]
[tex]$L=4 \sqrt{3}/3 cm[/tex]
Ab = n L a / 2
Substitute the values in the above equation, we get
[tex]$A_b=\frac{6 (4 \sqrt{3}/3)(2)}{2}[/tex]
[tex]$$A_b=24 \sqrt{3}/3 $$cm^2[/tex]
[tex]$A_b=8 \sqrt{3} cm^2[/tex]
[tex]V_p = A_b h[/tex]
substitute the values in the above equation, we get
[tex]$V_p=(8 \sqrt{3})(2)[/tex]
[tex]$V_p=16 \sqrt{3} cm^3[/tex]
[tex]$$V_p=16 (1.732) cm^3[/tex]
[tex]$$V_p=27.712 cm^3[/tex]
To estimate the volume of cylinder,
[tex]$V_c[/tex] = (π[tex]d^2[/tex]/4) h
Here, π = 3.14 and d = 1.6 cm
Height of the cylinder, h = t = 2 cm
substitute the values in the above equation, we get
[tex]$V_c=[3.14 (1.6) / 4] (2)[/tex]
[tex]$V_c=[3.14 (2.56) / 4] (2)[/tex]
[tex]$V_c=(2.0096) (2)[/tex]
[tex]$$V_c=4.019 cm^3[/tex]
Substitute the values in the equation, we get
[tex]$$V=V_p-V_c[/tex]
[tex]$$V=27.712 - 4.019[/tex]
[tex]$$V=23.693 cm^3[/tex]
[tex]$$V=23.6 cm^3[/tex]
Therefore, the volume of metal in the hex nut, to the nearest tenth exists [tex]$$23.6 cm^3[/tex].
To learn more about volume of cylinder and prism refer to:
https://brainly.com/question/12669337
#SPJ4
Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph?
Answers
The approximate solution to the given system of equation is (-2.71, 2.14)
Solving a system of linear equationsFrom the question, we are to determine the approximate solution to the given system of linear equations.
The given equations are
y = 0.5x + 3.5
y = -2/3 x+ 1/3
From the given information, we are to show the solutions on a graph
The graph that shows the solution to the given system of equation is shown below.
The solution to the given system is the point of intersection of the lines. The coordinate of the point of intersection of the lines is (-2.71, 2.14). That is, x = -2.71, y = 2.14.
Hence, the approximate solution to the given system of equation is (-2.71, 2.14)
Learn more on Solving systems of linear equations here: https://brainly.com/question/14323743
#SPJ1
What is the slope of the line that passes through the points (9, 2) and
(9,27)? Write your answer in simplest form.
Answers
Answer:
Slope (m) = infinity
Step-by-step explanation:
Given points:
⇒ (9, 2) and (9, 27)
In order to find the slope of these points, we must use the slope formula.
So the formula is ⇒ y₂ - y₁ / x₂ - x₁
Plug in the given points:
⇒ 27 - 2 / 9 - 9
Solve both the top and bottom (numerator and denominator):
⇒ 25 / 0
Divide:
⇒ Undefined.
(Anything divided by zero is undefined).
please help! find the distance of AG if A (4,4) and G (-1,-1)
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
By using distance formula :
[tex]\qquad \sf \dashrightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(4 - ( - 1)) {}^{2} + (4 - ( - 1)) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(4 + 1) {}^{2} + (4 + 1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2(5) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \sqrt{2 }\: \: units[/tex]
The distance between two points [tex]\rm{A(x_1,y_1)} [/tex] and [tex]\rm{B(x_2,y_2)}[/tex] is given by the formula,
[tex] \rm{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
Proof:
[tex] \rm{Let \: X'OX \: and \: YOY' \: be \: the \: z-axis \: and \: y-axis \: respectively. Then, O \: is \: the \: origin.}[/tex]
[tex] \rm{Let \: A(x_1,y_1) \: and \: B(x_2,y_2) \: be \: the \: given \: points.}[/tex]
[tex] \rm{Draw \: AL \perp \: OX, BM \perp \: OX \: and \: AN \perp BM }[/tex]
Now,
[tex] \rm{OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2}[/tex]
[tex]\rm\therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]
[tex] \: \: \: \: \rm{BN=(BM-NM)=(BM-AL)=(y_2-y_1)}[/tex]
[tex] \rm{In \: right \: angled \: \triangle ANB, by \: Pythagorean \: theorem,}[/tex]
We have,
[tex] \: \: \: \: \rm{AB^2=AN^2+BN^2}[/tex]
[tex] \rm{or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex] \rm\therefore AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
The Given question,
Find the distance of AG if A (4,4) and G (-1,-1).
Solution,
The given points are A(4,4) and G(-1,-1).
Then,
[tex] \rm{(x_1=4,y_1=4) and (x_2=-1,y_2=-1)}[/tex]
We know that,
The distance formula,
[tex] \rm{AG= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 1 - 4)}^{2} + {( - 1 - 4)}^{2} } [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 5)}^{2} + {( - 5)}^{2} } [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{25 + 25} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{50} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(25)} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(5)(5)} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)( {5}^{2}) } [/tex]
[tex] \rm \: \: \: \: \: \: \: \: = 5 \sqrt{2} \: units[/tex]
Answered by:
[tex]\frak{\red{moonlight123429}}[/tex]
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
Answers
For the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
Measures of a DataFrom the question, we are to determine the minimum, lower quartile, median, upper quartile, maximum, and interquartile range of the given data set
The given data set is
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Minimum = 48
Lower quartile = (54+56)/2
Lower quartile = 110/2
Lower quartile = 55
Median = (63+64)/2
Median = 127/2
Median = 63.5
Upper quartile = (74+74)/2
Upper quartile = 148/2
Upper quartile = 74
Maximum = 80
Interquartile range = Upper quartile - Lower quartile
Interquartile range = 74 - 55
Interquartile range = 19
Hence, for the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
Learn more on Measures of a Data here: https://brainly.com/question/15097997
#SPJ1
find the square roots of each of the following number
1: 81
2: 100
Answers
Multiply 9 with 9, and we get:
9 × 9 = 81
Multiply 10 with 10, and we get:
10 × 10 = 100
We get the final result as:
9²10²Hope this helps :)
PLLLLLEASE T_T PLLLEASE
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
let's solve ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{y - 6} + \cfrac{5}{y + 3} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4(y + 3) + 5(y - 6)}{(y - 6)(y + 3)} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4y + 12 + 5y - 30}{ {y}^{2} + 3y - 6y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{9y - 18}{ {y}^{2} - 3y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: 9y - 18 = 7y - 4[/tex]
[ denominator is same, so numerator must have same value to be equal ]
[tex]\qquad \sf \dashrightarrow \: 9y - 7y = - 4 + 18[/tex]
[tex]\qquad \sf \dashrightarrow \: 2y = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 7[/tex]
What is the area of the following polygon?
I have tried 24, 25 and 26 and none of worked and I am at a loss.
Answers
The area of the polygon is 25.5 square units
How to determine the area of the polygon?From the figure, we have the following coordinates
A = (-2, 1)
B = (3, 2)
C = (5, -3)
D = (-1, -3)
The area of the polygon is then calculated as:
A = 0.5 * |(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4)|
Substitute the known values in the above equation
Area = 0.5 * |(-2 * 2 - 3 * 1) + (3 * -3 - 5 * 2) + (5 * -3 + 1 * -3) + (-1 * 1 + 2 * -3)|
Evaluate the sum of products
Area = 0.5 * |-51|
Remove the absolute bracket
Area = 0.5 * 51
Evaluate the product
Area = 25.5
Hence, the area of the polygon is 25.5 square units
Read more about areas at:
https://brainly.com/question/25292087
#SPJ1
We can fill a certain barrel with water if we use water from 6 small pitchers, 3 medium pitchers, and one large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, how many of them do we need to fill the barrel?
Answers
Answer:
Solution Given:
let pitcher which is small be S medium be M and large be L and barrel be B.
By question
6S+3M+1L= 1B...... eq. 1
2S+1M+3L=1B.......eq. 2
The difference in 2L from the first to the second is 4S and 2M
Therefore, each L=2S+M
In equation 2
2S+1M+3L=1B
replacing 2S +1M by L,we get
L+3L=1B
4L=1B
Therefore, 4 large pitcher is required
Answer:
4 large pitchers
Step-by-step explanation:
Define the variables:
Let x = volume of a small pitcherLet y = volume of a medium pitcherLet z = volume of a large pitcherLet b = volume of a barrelCreate two equations with the given information and the defined variables.
Equation 1
If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:
⇒ 6x + 3y + z = b
Equation 2
If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:
⇒ 2x + y + 3z = b
Substitute Equation 2 into Equation 1
⇒ 6x + 3y + z = 2x + y + 3z
Subtract 6x from both sides:
⇒ 3y + z = -4x + y + 3z
Subtract y from both sides:
⇒ 2y + z = -4x + 3z
Subtract z from both sides:
⇒ 2y = -4x + 2z
Divide both sides by 2:
⇒ y = -2x + z
Substitute the found expression for y into Equation 1:
⇒ 6x + 3(-2x + z) + z = b
⇒ 6x - 6x + 3z + z = b
⇒ 4z = b
Therefore, 4 large pitchers are needed to fill the barrel.
Learn more about systems of equations here:
https://brainly.com/question/28093918
https://brainly.com/question/27034625
Please help right away
Answers
Answer:
A: (4,7)
B: (2,1)
C: (6,1)
Step-by-step explanation:
To plot the points, go along the x-axis (the horizontal line with the x on the end) and stop where the dot is. Whatever number the dot is above is the x-coordinate. Then, however many numbers you go up by to reach the dot is your y-coordinate.
hope this helps :)
Enter the correct answer in the box.
This graph represents a transformation of the parent square root function.
-10-8 -6
A
-2
10-
8
6-
2-
-2-
-4-
-6-
-8-
-10-
O
2
6 8 10
➜X
Replace the values of h and k to create the equation of the transformed function.
Answers
Answer:
Step-by-step explanation:
The most basic quadratic function is f(x) = x2, whose graph appears below. ... us to graph an entire family of quadratic functions using transformations.
[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answers
Answer:
x < -19/7
Step-by-step explanation:
Solve for x
2x+5 < (x+1)/4
Multiply each side by 4
4( 2x+5) < (x+1)/4 *4
8x + 20 < x+1
Subtract x from each side
8x+20-x < x+1-x
7x + 20 < 1
Subtract 20 from each side
7x+20-20 < 1-20
7x< -19
Divide by 7
7x/7 < -19/7
x < -19/7
Answer:
[tex] \red{x < \frac{ - 19}{7} }[/tex]
Step-by-step explanation:
[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]
Sketch The Graphs:
y = -1/3x -2
Answers
Answer:
Step-by-step explanation:
The graph of the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted. The graph is shown below.
A straight line is of the form y = mx + c, where m is the slope and c is the y-intercept.
To plot the given straight line [tex]y = -\frac{1}{3}x -2[/tex], follow the following steps:
Step 1: Substitute x = 0 in the given equation to obtain the point where the line intersects the y-axis.
y = 0 - 2
y = -2
The point at the y-axis is (0, -2).
Step 2: Substitute y = 0 in the given equation to obtain the point where the line intersects the x-axis.
[tex]0 = -\frac{1}{3}x -2\\x = -6[/tex]
The point at the x-axis is (-6, 0).
Step 3: Draw a straight line passing through both points.
Thus, the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted.
Learn more about Straight Line here;
https://brainly.com/question/31693341
#SPJ3
Find the measure of x.
16
X
38°
x = [?]
Round to the nearest hundredth.
Answers
The answer is.........
25.99
5. The grid shows how many eggs Ms. Benton bought.
The shaded boxes represent the number of eggs she
used to make the cookies. What percent and fraction
of the eggs bought were not used to make the cookies?
Show your work in the space below. Remember to
check your solution.
Answers
Answer:
You can count how many boxes that are not shaded to find how many eggs were not used, but that's to find out the fraction
Step-by-step explanation:
Count the boxes total in the grid. then count the number of boxes were not shaded. the number of total boxes is your denominator, and the number of boxes thar aren't shaded is your numerator.
I think...
Which of the following is equivalent to the quotient below?
√135/√3
A. 5√3
B. √45/3
C. 3√5
D. 3√15
Answers
The answer is C. 3√5.
√135/√3√45√3² × 53√5Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
Answers
Ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
(A) 49x2 -98x + 64yz +256y -2,831 = 0 (B) 81x2 -648x +100yz +200y -6,704 = 0 (F) 64x2 +512x +81y2 -324y -3,836 = 0What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.To identify the ellipses:
For the standard-form equation of an ellipse: Ax^2+Bx+Cy^2+Dy+E=0
We can define:
p=min(A,C)q=max(A,C)Then the eccentricity can be shown to be:
e=(1-p/q)p/q=1-e^2For Eccentricity<0.5, we want:
p/q>3/4Checking the values of p/q for the given equations, we have p/q= equations (A), (B), and (F) are of ellipses with eccentricity < 0.5.
Therefore, ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
(A) 49x2 -98x + 64yz +256y -2,831 = 0 (B) 81x2 -648x +100yz +200y -6,704 = 0 (F) 64x2 +512x +81y2 -324y -3,836 = 0Know more about equations here:
https://brainly.com/question/22688504
#SPJ4
The complete question is given below:
Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
(A) 49x2 -98x + 64yz +256y -2,831=0
(B) 81x2 -648x +100yz +200y -6,704 =0
(C) 6x2 -12x +54y2 +108y -426 =0
(D) 49x2 + 196x +36y2 +216y -1,244 =0
(E) 4x +32x +25y2 - 250y +589 =0
(F) 64x2 +512x +81y2 -324y -3,836 =0
Choose the equation that satisfies the data in the table.
-1 0 1
0
3
6
X
Y
OA. y = 3x +3
B.y = -x +9
Oc.y=x+9
OD. y=-3x +3
Answers
Answer:
A
Step-by-step explanation:
Based on the given table:
(x, y ) values are
(-1, 0)
(0, 3)
(1, 6)
A.
y = 3x+3, substitute each x and y pair in the equation to see if it checks
(x= -1, y= 0) (x= 0, y= 3) (x= 1, y= 6)
0 = -1·3+3 3 = 0·3 +3 6 = 1·3 + 3
0 = 0✅ 3 = 3✅ 6 = 6✅
Mr. jimenez deposited money into an account in which interest is compounded quarterly at a rate of 2.6%. how much did he deposit if the total amount in his account after 4 years was $7160.06, and he made no other deposits or withdrawals? $6455 $6455 $6798 $6798 $6887 $6887 $6977 $6977 skip to navigation
Answers
Answer:
$6455.
Step-by-step explanation:
The formula for this investment is:
A = P(1 + r/4)^4t where P = amount deposited , A amount after t years,
r = rate (as a decimal fraction).
So we have:
7160.06 = P(1 + 0.026/4)^16
7160.06 = P * 1.109227
P = 7160.06 / 1.109227
= $6455.
creating holes in the sand to fill the varied buckets is an example of an inverse relationship
true or false
Answers
Answer:
True
Step-by-step explanation:
You are taking away sand from the ground and adding sand to the bucket. There is less sand on the ground and more in the bucket making it inverse.
Answers are needed urgently..ty
Answers
Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.
The length of the straight line AB = 80cm
Calculation of angle of a triangleThe angle at a point = 360°
Angle AQB= 360 - 210° = 150
But the angle that makes up a triangle= 180°
180-150= 30°
But <QAB = <QBA because triangle AQB is an isosceles triangle.
30/2 = 15°
To calculate the length of the straight line the following is carried out using the sine laws.
a/ sina, = b sinb
a= 8cm, sin a { sin 15)
b= ? , sin B = 150
make b the subject formula;
8/sin15= b/sin 150
b= 8 × sin 150/sin 15
b= 80cm
Learn more about isosceles triangle here:
https://brainly.com/question/25812711
#SPJ1
sariah has just begun training for a half-marathon, which is 13.1 miles. since she was on vacation, she started the training program later than the rest of her running club. There are 6 weeks of training runs remaining before the race.
In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week. If she continues to increase the length of her runs the same way, will there be enough time left in the train program for her to get up to half-marathon distance?
Describe how you would solve this problem using Polya’s four-step problem-solving method. Complete each task as part of your response. Be sure to number task 1-task 4 so that your instructor can tell which part you are answering.
1. understand the problem
task 1: read the problem and restate in your own words what the question asks.
2. formulate a plan
task 2: identify the model you would use to represent the problem and explain why you chose the model.
3. implement the plan
task 3: solve the problem and state your answer.
4. review the results
task 4: explain your problem-solving process and how you know your answer is correct.
Answers
There would not be enough time to reach the half marathon distance.
Would there be enough time to reach the half marathon distance?The distance run in a week can be represented with a linear equation. A linear equation is an equation that has a single variable raised to the power of 1.
The linear equation that would be used to represent the distance run would be in the form:
Miles run in a week = miles run the previous week - increase in miles
Increase in miles = 6 - 4.5 = 1.5 miles
Miles run in the fourth week = 1.5 + 6 = 7.5 miles
Miles run in the fifth week = 7.5 miles + 1.5 miles = 9 miles
Miles run in the sixth week = 9 + 1.5 = 10.5 miles
There would not be enough time to reach the half marathon distance because in the sixth week she would be able to run 10.50 miles
To learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
Andre says that [tex]log_10(55)=1.5[/tex] because 55 is halfway between 10 and 100. Do you agree with Andre? Explain your reasoning.
I know that answer is false, but I don't know how to explain!!
Answers
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllllllll} \log_{\underline{10}}(10)=1&\implies &\underline{10}^1=10 ~~ \checkmark\\\\ \log_{10}(100)=2&\implies &10^2=100~~ \checkmark\\\\ \log_{10}(55)=1.5&\implies &10^{1.5}=55\implies 10^{\frac{3}{2}}=55\implies \sqrt[2]{10^3}=55\\\\ &&\sqrt{1000}\ne 55 ~~ \bigotimes \end{array}[/tex]
increments over the exponent, are not directly proportional to increments on the resulting values, namely the half-way from 10² and 10⁴ is not 10³, because 10⁴ is 100 times 10², and 10³ is simply 10 times 10².