Answers
Answer:
D
Step-by-step explanation:
given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the turning point ( vertex ) is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = 2x² + 4x - 3 ← is in standard form
with a = 2, b = 4 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{4}{2(2)}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1
substitute x = - 1 into the equation for corresponding y- coordinate
y = 2(- 1)² + 4(- 1) - 3 = 2(1) - 4 - 3 = 2 - 7 = - 5
turning point = (- 1, - 5 )
Answer:
The Correct answer is D
(-1,-5)
Related Questions
given the vertex at (-4, 5) and a-value of 5, write the vertex form of the quadratic equation.
Answers
The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex.
To write the vertex form of a quadratic equation given the vertex (-4, 5) and a-value of 5, you can use the vertex form equation:
y = a(x - h)² + k
where (h, k) is the vertex and a is the a-value.
In this case, h = -4, k = 5, and a = 5. Substitute these values into the equation:
y = 5(x - (-4))² + 5
Simplify the equation:
y = 5(x + 4)² + 5
So, the vertex form of the quadratic equation is:
y = 5(x + 4)² + 5
Learn more about quadratic equation here: brainly.com/question/30098550
#SPJ11
The vertex form of the quadratic equation is: y = 5[tex](x + 4 )^2[/tex] + 5
A quadratic equation's vertex form is provided by:
y = a[tex](x - h)^2[/tex] + k
where "a" is the coefficient of the parabola and "(h, k)" is its vertex [tex]x^2.[/tex]
Given that the vertex is (-4, 5) and a-value is 5, we can substitute the values into the vertex form equation:
h = -4
k = 5
a = 5
When we enter these numbers into the equation, we obtain:
y = 5(x -[tex](-4) ^2[/tex] + 5
Simplifying the equation, we get:
y = 5[tex](x + 4)^2[/tex] + 5
So, the vertex form of the quadratic equation is:
y = 5[tex](x + 4 )^2[/tex] + 5
Learn more about “ quadratic equation “ visit here;
https://brainly.com/question/30098550
#SPJ4
16^5+16^4 is divisible by 17
Answers
Given that,
165 + 161
is divisible by 17.
According to the question,
To determine 165 + 161
is divisible by 17 following all the steps given below.
Rewrite the function and solving,
= 16° + 161
= 16 x 16 x 16 x 16 × 16 + 16 × 16 × 16 × 16 × 16
= 1048576 + 65536
= 68, 719, 476, 736
Therefore,
68, 719, 476, 736
17
= 4, 042, 322, 160.94
Hence, Yes it is divisible by 17.
12. Jenny's water bottle holds 1.3 liters of water. How many milliliters of water does the water bottle hold? milliliters
Answers
Answer:
1300 milliliters
Step-by-step explanation:
There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.
the mesures of two suplementary angles are (1/2x) and (x+30) betermine te value of x
Answers
x = 100
Step-by-step Explanation:
Supplementary angles add up to 180 degrees, so we can set up the equation:
(1/2x) + (x + 30) = 180
To solve for x, we can start by simplifying the left side of the equation by combining the terms:
(1/2x) + x + 30 = 180
Multiplying both sides of the equation by 2 to eliminate the fraction:
1x + 2(x + 30) = 360
Simplifying the right side of the equation:
1x + 2x + 60 = 360
Combining like terms:
3x + 60 = 360
Subtracting 60 from both sides of the equation:
3x = 300
Dividing both sides of the equation by 3:
x = 100
Therefore, the value of x is 100.
Further explanation:
Supplementary angles are two angles whose sum is 180 degrees. Let's use this fact to form an equation with the given measures:
(1/2x) + (x+30) = 180
To solve for x, we need to isolate it on one side of the equation. Let's start by simplifying the left side:
1/2x + x + 30 = 180
3/2x + 30 = 180
3/2x = 150
x = 100
Therefore, the value of x is 100. To check this result, we can substitute x=100 into the original measures:
(1/2x) = 50
(x+30) = 130
And indeed, 50 and 130 are supplementary angles whose sum is 180.
What is the solution to the inequality -0.4x 1.27> 0.8
Answers
Answer:
x < 1.175
Step-by-step explanation:
-0.4x + 1.27 > 0.8
-0.4x > -0.47
x < 1.175
Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answers
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
Learn more about graphs at
https://brainly.com/question/19040584
#SPJ1
Just look at the photo and anything you can help me with wi be much appreciated
Answers
10.
a.
120*0.60=72
120+72=192
answer: 192
b.
192*0.30=57.60
192-57.60=134.40
answer: 134.40
c.
134.40-120= 14.40
the store made $14.40 on the bicycle
11.
147*0.75=110.25
147-110.25=36.75
answer: 36.75
12.
a.
60*0.06=3.60
60+3.60= 63.60
answer: 63.60
b.
60*0.15=9
60-9=51
answer: 51
c.
51*0.06=3.06
51+3.06=54.06
answer: 54.06
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Answers
The activity with a central angle of 54° is Kayaking and there were about 557 principals in attendance based on the prediction
The activity with a central angle of 54°The formula to calculate the central angle for an activity is:
central angle = (number of campers for the activity / total number of campers) x 360°
Using this formula, we can calculate the central angle for each activity:
Kayaking: (15/100) x 360° = 54°
Wakeboarding: (11/100) x 360° = 39.6°
Windsurfing: (7/100) x 360° = 25.2°
Waterskiing: (13/100) x 360° = 46.8°
Paddleboarding: (54/100) x 360° = 194.4°
Therefore, the activity with a central angle of 54° is Kayaking.
Predicting the number of principals in attendance at the conference?To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.
In the exhibit room, out of 70 people, 52 were principals.
So, the proportion of principals in the exhibit room was 52/70
We can predict the number of principals in attendance at the conference as follows:
Number of principals = proportion of principals x total number of attendees
If we plug in the values, we get:
number of principals = 52/70 x 750 = 557
So, based on this prediction, we can say that there were 557 principals in attendance at the conference.
Read more about proportion at
https://brainly.com/question/1781657
#SPJ1
5. A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. (Lesson 5-13)
b. Find the volume of the cone.
c. What fraction of the cylinder's volume is the cone's volume?
Answers
V = (1/3)π(3^2)(5) = 15π cubic inches
c. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 3 inches and the height is 5 inches, so the volume of the cylinder is:
V = π(3^2)(5) = 45π cubic inches
The fraction of the cylinder's volume that is the cone's volume can be found by dividing the volume of the cone by the volume of the cylinder:
(15π) / (45π) = 1/3
Therefore, the cone's volume is 1/3 of the cylinder's volume.
you need to answer every question and you get 25pts and brainliest
Answers
Using probability, we can find the following:
a. In the figure.
b. The probability that the first set is green is = 0.8
c. Probability that the second set is green is = 0.06
d. The probability that both the sets are green is = 0.48
e. The probability that at least one set is green is = 0.86
Define probability?The likelihood that an event will occur is described by probability. There are many circumstances in real life where we may need to foresee how something will turn out. We might be able to predict the outcome of an event or we might not. At this point, we say, "There is a chance that the event will happen or not."
Here in the question,
b.
The probability that the first set is green is:
P = 1 - 0.2
= 0.8
c.
Now the first set is given as not green.
Probability that the second set is green is:
p = 0.2 × 0.3
= 0.06
d.
Now probability that both the sets are green is:
P = 0.8 × 0.6
= 0.48
e.
When both the sets are not green, probability is:
0.2 × 0.7
= 0.14
So, probability that at least one set is green is:
P = 1- 0.14
= 0.86
To know more about probability, visit:
https://brainly.com/question/16484393
#SPJ1
The histogram below shows the results of a survey on the number of traffic tickets received by a random group of drivers. 3 86 76 51 Number of People A 1 9 2 Traffic Tickets 10 8 6 Number of Traffic Tickets Step 6: How many people received either 4 or 5 traffic tickets? 12
Answers
In reference to the given histogram, an absence of bars signifying either 4 or 5 traffic tickets implies that no one from the selection had accumulated this amount.
How to explain the histogramIt should be noted that to make sure our point is accurate, we can sum the heights of the separate bars for 3, 6 and 8 tickets which demonstrate the total people included within the survey who have acquired the relevant number of traffic citations.
The height of the bar for three violations measures out at 1.
Conversely, a measurement of 2 denotes the bar for six infringements.
An assessment of 1 has been given to the bar with regards to eight offences.
Due to the lack of representation mentioned in the histogram concerning both 4 and 5 transgressions, it confirms our inference: nobody from the selection received four or five traffic tickets.
Learn more about histogram on
https://brainly.com/question/2962546
#SPJ1
Find the value of x and y in each triangle
Answers
Answer:
x=4 y=3
Step-by-step explanation:
because y=3 and x=4
Find the equation of the line that is perpendicular to the line AB and passes through the point. (0,2)
Answers
The equation of a line perpendicular to line AB and passing through point (0,2) is y = -4x + 2.
The given line has a slope of 1/4, so the slope of any line perpendicular to it will be -4 (the negative reciprocal).
Using the point-slope form of a line, we can write the equation of the line passing through the point (0,2) with slope -4 as
y - 2 = -4(x - 0)
Simplifying, we get
y - 2 = -4x
Adding 2 to both sides, we get
y = -4x + 2
Therefore, the equation of the line passing through the point (0,2) which is perpendicular to the line y=1/4x+5 is y = -4x + 2.
To know more about Equation of line:
https://brainly.com/question/21511618
#SPJ1
Help, please, is for today.
Answers
Measure of angle 2= 62 degrees
Step by Step:
The ratio of the angles is 1:2
So you add 1+2=3
Then divide 102/3, which equals 34
Finally multiply 34*2 to get 68
Suppose 15% of x equals 20% of y. What percentage of x is y?
A 5
B 35
C 75
D 133 1/3
E 300
Answers
If 15% of "x" is 20% of "y", then "y" is 75 percent of "x", the correct option is (c).
The "Percentage" is defined as a way to express the proportions or rates in terms of a "relative-scale" out of 100,
We know that, 15% of "x" equals 20% of "y".
Mathematically, this can be expressed as,
0.15x = 0.20y, ...because 15% = 0.15 and 20% = 0.20;
To find what percentage of x is y, we need to express "y" as a percentage of "x".
On solving further,
We get,
⇒ 0.15x = 0.20y,
⇒ y = (0.15x)/0.20,
⇒ y = 0.75x
It is read as "y" is read as 75% of "x".
Therefore, "y" is 0.75 times "x", or 75% of "x", Option(c) is correct.
Learn more about Percentage here
https://brainly.com/question/19733442
#SPJ4
(a) Three squares have the areas of 7 cm², 17 cm² and 10 cm², (i) Will the squares exactly surround a right angled triangle? (ii) Explain your answer.
Answers
Answer:
(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Step-by-step explanation:
To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:
a² = 7 cm²
b² = 17 cm²
c² = 10 cm²
We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.
We can rearrange the equations above to solve for a, b, and c:
a = √7 cm ≈ 2.65 cm
b = √17 cm ≈ 4.12 cm
c = √10 cm ≈ 3.16 cm
Now, we can check whether the Pythagorean theorem holds:
c² = a² + b²
(√10 cm)² = (√7 cm)² + (√17 cm)²
10 cm = 7 cm + 17 cm
This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
convert 180⁰ in to grades
Answers
Answer: 9/10
Step-by-step explanation:
Randy is designing a circular garden that is 18 feet in diameter. He is buying plastic edging that costs $1. 50 per foot. He can only buy edging in whole-foot amounts. How much does it cost Randy to buy edging for his garden? Use 3. 14 for pie.
Answers
If the diameter of circular-garden is 18 feet, then it will cost Randy an amount of $85.50 to buy edges for his garden.
The "Circumference" of circle is defined as the "total-length" of the boundary or the outer edge of the circle.
The circumference formula is : Circumference = π × Diameter,
The "diameter" of garden is = 18-feet,
So, Circumference = 3.14 × 18 = 56.52 feet,
Since, Randy needs to buy plastic-edging to cover the entire circumference of garden, he needs to buy 56.52 feet of edging.
We know that, Randy can only buy edging in whole-foot amounts,
So, rounding up to the nearest whole foot, we get 57 feet,
The cost of edging is = $1.50 per foot,
So, "total-cost" for Randy to buy edging for his garden is,
⇒ Total Cost = (Cost per foot) × (Number of feet),
⇒ $1.50 × 57,
⇒ $85.50
Therefore, it will cost Randy $85.50 to buy edging for his circular garden.
Learn more about Circumference here
https://brainly.com/question/16125353
#SPJ4
Find the value of x. If a segment looks like a tangent, it is a tangent.
Answers
We got x = 149.53 by using Pythagorean theorem.
What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90°.
[tex]172^2=85^2+x^2[/tex]
[tex]29584=7225+x^2[/tex]
[tex]x^2=29584-7225[/tex]
[tex]=22359[/tex]
[tex]x=\sqrt{22359}[/tex]
[tex]\boxed{\bold{x=149.53}}[/tex]
Learn more about Pythagorean theorem:
brainly.com/question/14930619
An angle measures 56.8° less than the measure of its complementary angle. What is the
measure of each angle?
Answers
We know that the measure of its complementary angle is 90 - x degrees.
According to the problem, the angle measures 56.8 degrees less than its complementary angle.
So:
x = (90 - x) - 56.8
Solving for x:
2x = 90 - 56.8
2x = 33.2
x = 16.6
Therefore, the angle measures 16.6 degrees and its complementary angle measures 73.4 degrees.
Find the area of the circle. Round your answer to the nearest hundredth. Use $3.14$ or $\frac{22}{7}$
for $\pi$ .
area: about
ft2
Answers
The area of the given circle is 1.76625 square feet.
How to find the area of the circle?Remember that the area of a circle of radius R is given by the formula:
A = pi*R²
Where pi = 3.14
Here we know the diameter (2 times the radius) of the circle, which is 1.5ft, then the radius is:
R = 1.5ft/2 = 0.75ft
Then the area of the circle is:
A = 3.14*(0.75ft)²
A = 1.76625 ft²
Learn more about area at:
https://brainly.com/question/24487155
#SPJ1
how do i solve this??
Answers
Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answers
Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.
Explain about the Histogram:A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of dataset in a series of equal-sized numerical intervals.
The independent variable is represented is along horizontal axis and indeed the dependent variable is plotted along of the vertical axis in the most popular type of histogram.A histogram is a type of bar graph that displays how frequently something occurs over a range of time. Histograms compare a variety of data, as opposed to bar graphs, which compare defined amounts.Given that-
The most efficient sort of graphic to show the data would be a histogram.A histogram is an illustration of a graph that shows the proportion of data points within such a range of values.It is a useful tool for showing data distribution and also can aid in the identification of trends and patterns.The best sort of graph to use is a histogram because it displays the frequency of data points.Thus, Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.
Know more about the Histogram
https://brainly.com/question/28164315
#SPJ1
please help needed like rn
Answers
An equation in slope-intercept form for the line shown in the graph is x = -1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 3)/(-1 + 1)
Slope (m) = -3/0
Slope (m) = 0.
At data point (-1, 3) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 0(x - (-1))
y - 3 = 0
y = 3.
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
SARA WANTS TO SAVE $1600 IN 8 MONTHS, HOW MUCH DOES SARA NEEEDS TO SAVE MONTHLY?
Answers
Answer:
$200
Step-by-step explanation:
Just divide 1600 by 8
1600 ÷ 8 = 200
Answer:
sara needs to save 200 monthly
Step-by-step explanation:
i just divided 1600 by 8.
hope u have a great day!!
Marcellus and Anika are playing a video game where they earn 35 stars for each level they pass. Which equation represents the total number of stars earned, y, for passing x levels?
Answers
The equation represents the total number of stars is y = 35x
Which equation represents the total number of starsThe equation that represents the total number of stars earned, y, for passing x levels would be:
y = 35x
where y represents the total number of stars earned, and x represents the number of levels passed.
For example, if Marcellus and Anika passed 10 levels, they would earn:
y = 35(10) = 350 stars
Read more about linear equations at
https://brainly.com/question/18831322
#SPJ1
[tex]7\sqrt[3]{7}-\sqrt[3]{128}[/tex]
Answers
The expression 7∛7 - ∛128 is: 49∛7 - 8∛2.
What is the expression?We can simplify this expression using the fact that ∛(a * b) = ∛a * ∛b and ∛(a^3) = a.
First, let's factor ∛128 into prime factors: ∛128 = ∛(2^7) = 2 * ∛(2^5) = 2 * ∛(32).
Next, we can simplify 7∛7 as much as possible:
7∛7 = ∛(7^3) * ∛7 = 7∛(7^2) * ∛7 = 7 * 7∛7.
Now we can substitute these simplifications into the original expression:
7∛7 - ∛128 = 7 * 7∛7 - 2 * ∛32
We can simplify ∛32 as follows:
∛32 = ∛(2^5) = 2 * ∛(2^2) = 4∛2
Now, we can substitute this back into the expression:
7 * 7∛7 - 2 * ∛32 = 7 * 7∛7 - 2 * 4∛2
= 49∛7 - 8∛2
So the simplified expression is 49∛7 - 8∛2.
Learn more about expression here:https://brainly.com/question/1859113
#SPJ1
HELPPP ASAPPPPP What is the surface area of the square pyramid represented by the net?
Enter your answer in the box.
m²
Answers
Answer:
144 m²
Step-by-step explanation:
You want to know the surface area of a square base pyramid with a side length of 6 m and a slant height of 9 m.
Surface areaThe area of the given net is the sum of the areas of 4 congruent triangles and one square. The areas of these can be found using the relevant formulas.
SA = square area + 4 × triangle area
SA = 6² + 4 × 1/2(6)(9) = 36 +108
SA = 144 . . . . square meters
__
Additional comment
The area of a square of side s is A = s².
The area of a triangle with base b and height h is A = 1/2bh.
a food shop offers 5 different sandwiches and 8 different drink choices. how many choices are possible for a single sandwich and a drink?
Answers
Answer:
Step-by-step explanation:
5
Can someone help me a little so I can learn this
Answers
Answer:b
Step-by-step explanation:
Answer:
b and c
Step-by-step explanation:
b 5(7+6s—9t)
35+30s—45
c 10×(3.5+3s—4.5t)
10×3.5 +10×3s—10×4.5t
35+30s—45t