Answer:
white=10/17
red=4/17
black=3/17
hope it helps you
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Which inequality in vertex form represents the region less than the quadratic function with vertex (-2, 2) and includes the point (-4, 14) on the boundary?
The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)
What is the inequality associated to a given statement
The standard form of the equation of the parabola is defined by the following expression:
y - k = C · (x - h)² (1)
Where:
h, k - VertexC - Vertex constantNow we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)
14 - 2 = C · [- 4 - (- 2)]²
12 = C · (-2)
C = - 6
The equation of the parabola in vertex form is
y - 2 = - 6 · (x + 2)²
y = - 6 · (x + 2)² + 2
Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)
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Answer:
y < 3(x + 2)2 + 2
Step-by-step explanation:
just do it
On a ΔABC, mΔA=80, mΔB=60
Find mΔC
The measure of angle C (m ∠C) is 40°
Calculating angles in a triangleFrom the question, we are to determine the measure of angle C (m ∠C)
In any given triangle, the sum of all the angles is 180°
Thus,
In ΔABC, the angles sum up to 180°
That is,
∠A + ∠B + ∠C = 180°
From the given information,
m ∠A = 80°, m ∠B = 60°
Thus,
80° + 60° + m ∠C = 180°
140° + m ∠C = 180°
m ∠C = 180° - 140°
m ∠C = 40°
Hence, the measure of angle C (m ∠C) is 40°
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Find the area of the regular polygon. Round to the nearest tenth
Answer:
1/2×base×height
1/2×8×8
32cm²
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Proving a uadrilateral is a Parallelogram
Assignment Active
Determining Side Lengths in a Parallelogram
In quadrilateral ABCD, AD 1, BC.
3x+7
D
A
B
5x-9
What must the length of segment AD be for the
quadrilateral to be a parallelogram?
O 8 units
O 16 units
O 31 units
O 62 units
Answer:
31 units
Step-by-step explanation:
If a quadrilateral has a pair of sides that is both parallel and congruent, then the quadrilateral is a parallelogram.
Sides AD and BC are given as parallel.
If they are also congruent, then quadrilateral ABCD is a parallelogram.
3x + 7 = 5x - 9
-2x = -16
x = 8
AD = 3x + 7
AD = 3(8) + 7
AD = 31
Answer: 31 units
find each lettered angel measure
Answer:
a = 64°
b = 138.7°
Step-by-step explanation:
First, Let's find the measure a,
180° = 116° + a180 - 116 = aa = 64°______
Now,
90° + a + 82° + x + x + x = 360°90+ 64 + 82 + 3x = 360° 236 + 3x = 360 3x = 124/ 3x = 41.3°______
Now that we found out what x equals, let's find 'b'-
b + x = 180°b + 41.3 = 180b = 180 - 41.3b = 138.7°kindly solve these questions for me.
The perimeter of the rectangle based on the factors given is 46.
How to calculate the perimeter?The area of the rectangle is given as (x² + 13x - 90). This will be:
= (x² + 13x - 90)
= x² + 18x - 5x - 90
= x(x + 18) - 5(x + 18)
= (x - 5)(x + 18)
The sides of the rectangle are 5 and 18. The perimeter will be:
= 2(l + w)
= 2(5 + 18)
= 46
The area of the rectangle is given as (x² + 24x - 81.
= (x² + 24x - 81)
= x² + 27x - 3x - 81
= x(x + 27) - 3(x + 27)
= (x - 3)(x + 27)
The sides are 3 and 27. The perimeter will be:
= 2(l + w)
= 2(27 + 3)
= 60
= (x + 1)² + 3(x + 1) + 2
= (x + 1)(x + 1) + 3x + 3 + 2
= x² + x + x + 1 + 3x + 5
= x² + 5x + 6
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find the slope of this line.
Answer:
4/5
Step-by-step explanation:
SImply use slope formula. We see the graph has defined points at (5, 4), and (-5, -4).
m=(Y2-Y1)/(X2-X1)
(4-(-4))/(5-(-5))=8/10
Simplify 8/10
=4/5
Which point is the center of the Circle with the given equation.
(x + 5)2 + (y - 4)2 = 9
The center of the circle is (-5, 4)
How to determine the center of the circle?The circle equation is given as:
(x + 5)^2 + (y - 4)^2 = 9
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Center = (a, b)
By comparing both equations, we have
(a, b) = (-5, 4)
Hence, the center of the circle is (-5, 4)
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Find the point on the line y = 5x + 2 that is closest to the origin.
Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
Step-by-step explanation:
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]
Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.
Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)
[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]
Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.
[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]
Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]
[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]
The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The given equation of a line is y=5x+2 ------(I)
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
So, slope of perpendicular line is -1/5
The equation of the point slope form is: (y - y1) = m(x - x1)
Now, substitute m=-1/5 and (x, y)=(0, 0), we get
y-0=-1/5 (x-0)
y=-1/5 x -----(II)
Equate equation (I) and (II), we get
5x+2=-1/5 x
⇒ -x=25x+10
⇒ -26x=10
⇒ x= -5/13
So, y=-1/5 x =1/13
Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
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A cylinder has a olive of 200mm and a height of 17mm. The volume formula for a cylinder is
The radius of the given cylinder with a volume of 200 mm³ and a height of 17mm is: 1.93 mm.
How to find the Volume of a Cylinder?The formula for finding the volume of any cylinder is given as: πr²h, where r is the radius and h is the height of the cylinder.
Given the following:
Volume = 200 mm³
Height (h) = 17 mm
Radius (r) = ?
Plug the values into the formula for volume
πr²(17) = 200
r² = 200/17π
r² = 3.74
r = 1.93 mm
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use the sum to product formula to find exact values: if cos255 - cos195 = squrtroot a/ 2 then a=
By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2
How to analyze a trigonometric expression
In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:
[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]
Then,
cos 255° - cos 195° = - 2 · sin 225° · sin 30°
cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°
cos 255° - cos 195° = 2 · sin 135° · sin 30°
cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)
cos 255° - cos 195° = √2 / 2
Then, by direct comparison we find that a = 2.
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Rafael earns $35 more per week than Andrew. If their weekly salaries total $715, what amount does each earn?
Answer:
Rafael earns $375
Andrew earns $340
Step-by-step explanation:
Here, we will set up a system of equations where r represents Rafael and a represents andrew.
r = a + 35
r + a = 715
Next, we substitute a + 35 for r in the second equation.
(a + 35) + a = 715 (combine like terms)
2a + 35 = 715 (subtract 35 from both sides)
2a = 680 (divide both sides by 2)
a = 340
To solve for r, we can plug 340 for a into either equation.
r = (340) + 35
r = 375
We can double check by plugging both values into the other equation.
375 + 340 = 715 (yes, it works!)
Brainliest, please :)
Tanisha is signing up for a gym membership with a one-time fee to join and then a
monthly fee to remain a member. The monthly fee is $50 and the one-time joining
fee is $100. Make a table of values and then write an equation for C, in terms of t,
representing the total cost of the gym membership over t months.
Answer:
t=150
Step-by-step explanation:
50+100=150
50×12=600
Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
3x4
Name? [?]
Degree? [ ]
Answer:
monopoly, order 1
Step-by-step explanation:
because the x has just power of one that is why is monopoly and in order 1
A sience teacher uses an overhead projector to display a diagram of a pulley sytem. the actual diagram is 6'' by 7.2''. The image projected onto the wall is 4' 2'' by 5'' what is the scale factor of the projection
Answer:
25/36, or .694444
Step-by-step explanation:
First, let's convert 6" to inches.
That gives us 72. After we convert 4'2" into inches, we get 50.
This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:
50/72 = 25/36 = .6944444
Which is the graph of the function f(x)=√x?
The graph is shown in the attached image.
Sketch the graph of the equation y=2/3 x+2 and label three points on the graph.
Answer:
Step-by-step explanation:
(0,2)
Answer:
Step-by-step explanation
So, the graph goes through the points, (-3,0) and (2,0). 3 points on the graph can be (-3,0), (2,0), and (4,3)
An employee worked for 8 hours on 2 days, 6 hours on 1 day, and 4 hours on 2 day
What is the average number of hours the employee worked per day?
A.) 6.0
B.) 6.5
C.) 7.0
D.) 7.5
E.) 8.0
Answer:
A) 6.0
Step-by-step explanation:
First, total amount of hours, since average is sum of the numbers by how many numbers there is.
Day 1=8x2 hr
Day 2=6x1 hr
Day 3=4x2 hr
which is, 16+6+8=30
then divide 30 by how many days there is, which is 5 days.
30/5=6
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Using the z-distribution, the test statistic is:
c) -2.63.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, we test if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex].[tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex].For the distribution of differences, it is given by:
[tex]\overline{x} = \mu_D - \mu_C = 12 - 14 = -2[/tex].[tex]s = \sqrt{s_D^2 + s_C^2} = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
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Is this figure a polygon? Explain.
Which person has a dept ratio that is higher the 18%
the person with the debt ratio that is higher than 18% can be found by dividing the person's debt by their income .
what is the debt ratio?the necessary information is not given so a general explanation will be given.
the debt ratio is found by the formula:
= monthly debt payment / monthly gross income
this figure allows creditors to see if a person can affort to incur more debt based on how much of their gross monthly income is being used to service debt.
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A rectangular lot has a perimeter of 80 meters and a length of 25 meters. Find the
width of the lot.
Fence->
25m
Meters
W
Answer:
15m
Step-by-step explanation:
Let w be the width, l the length and p the perimeter.
We know, by definition, that p = 2w + 2l. We also know that p = 80m and l = 25m.
So we can re-write the perimeter formula as:
80 = 2w + 50
2w = 30
w = 15m
So we now know that the width is 15m.
Which of the following choices will simplify 5-3•2?
a local newspaper assigns a rating between 1 and 10 to every book and movie it reviews. Victor gathered data about five titles where the newspaper reviewed both the book and the movie version of the title. The ratings assigned by the newspaper are given in the table. Select the points that represent this data.
The points that represent this data are shown in the image attached below.
What is a scatter plot?A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided in table above, the points that represent this data are shown in the image attached below.
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Answer:
please look at the picture
What common base can be used to rewrite each side of the equation 2^x+3-3=5
The common base that can be used to rewrite each side of the equation is 2.
How to find the common base used to rewrite each equation?The common base that can be used to rewrite each side of the equation is as follows:
2ˣ⁺³ - 3 = 5
add 3 to both sides
2ˣ⁺³ - 3 + 3 = 5 + 3
2ˣ⁺³ = 8
Hence,
2ˣ⁺³ = 2³
Therefore, the common base that can be used to rewrite each side of the equation is 2.
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D
C
63. If AD 20 centimeters, DC= 15 centimeters,
BC=7 centimeters, and AB = 24 centimeters,
what is the area of quadrilateral ABCD?
A. 66 sq cm
B.
B
117 sq cm
C. 234 sq cm
D.
468 sq cm
The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)
What is the area of the quadrilateral?
Herein we have a description of an irregular quadrilateral, whose area must be determined by adding the areas of minor quadrilaterals and triangles that are part of it. The area is now determined:
A = 0.5 · (24 cm) · (7 cm) + 0.5 · (15 cm) · (20 cm)
A = 234 cm²
The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)
Remark
The picture with the quadrilateral is missing and is included as attachment.
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When Billy's asked how old he is, he replies, "In two years I will be twice as old as I was five years ago." How old is he?
brainliest to whoever answers
Answer:
12 years old
Step-by-step explanation:
Set up the following equation:
x + 2 = 2(x - 5) (distribute the 2)
x + 2 = 2x - 10 (subtract 2 from both sides)
x = 2x - 12 (subtract 2x from both sides)
-x = -12 (multiply both sides by negative 1)
x = 12
Brainliest, please :)
Answer: 12
Step-by-step explanation:
Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.
The phrase "in two years" means when his age is 2 more than his current age, or x + 2.
The phrase "same as" represents equality. The expressions on both sides have the same value.
The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).
Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:
[tex]x+2=2(x-5)[/tex]
[tex]x+2=2x-10[/tex] [Distributive Property]
[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]
[tex]-x=-12[/tex] [Combining like terms and simplifying]
[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]
Hence, Billy's age is 12.
Simplify (x + 5)2 using the square of a binomial formula.
x² + 10x + 25
x²-10X-25
x²-10x+25
x² + 10x - 25
Answer:
[tex]x^2 + 10x + 25[/tex]
Step-by-step explanation:
Hello!
Formula: [tex](a +b)^2 = a^2 + 2ab + b^2[/tex]
a = xb = 5Plug it into the formula and simplify.
Simplify[tex](a +b)^2 = a^2 + 2ab + b^2[/tex][tex](x +5)^2 = x^2 + 2(x)(5) + 5^2[/tex][tex](x +5)^2 = x^2 + 10x + 25[/tex]The answer is the first option: [tex]x^2 + 10x + 25[/tex].
Answer:
x^2-10x+25
Step-by-step explanation:
This is the correct answer
According to the general equation for conditional probability, if P(AB) = and P(B) = 2, what is P(A/B)? 12 O A. 3/ О в. 4 O c. 2/ C. 5 O D. 9
Using conditional probability, it is found that:
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.For this problem, we are given that:
[tex]P(B^\prime) = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}[/tex].[tex]P(A \cap B^\prime) = \frac{2}{9}[/tex]Then:
[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]
[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
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3. A line with a slope of passes through the point (10,-5).
The equation of the line in slope intercept form
can be given by the formula y = mx + b
where m=
and b =
√x
The equation of the line is y = -3/2x + 10
How to determine the line equation?The given parameters are:
Slope, m = -3/2
Point, (x, y) = (10, -5)
The line equation is represented as
y = mx + b
Substitute the given parameters in the equation
-5 = -3/2 * 10 + b
This gives
-5 = -15 + b
Add 15 to both sides
b = 10
So, we have:
y = -3/2x + 10
Hence, the equation of the line is y = -3/2x + 10
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