5x - 3 = 7
Add 3 to both sides.
5x = 10
Divide both sides by 5.
x = 2
The value of x is 2.
Given a quadratic function, y = ax^{2} + bx + c, what happens to the graph when "a" is positive?.
Answer:
So, given a quadratic function, y = ax2 + bx + c, when "a" is positive, the parabola opens upward and the vertex is the minimum value. On the other hand, if "a" is negative, the graph opens downward and the vertex is the maximum value.
Step-by-step explanation:
100% on edg :)
The quadratic function, y = ax²+ bx + c opening upward if the value of 'a' is positive.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have quadratic function,
y = ax² + bx + c
If the value of 'a' is negative, then the function will be opening downside and if the value of 'a' is positive, then the function will be opening upside.
Let say a = 1, b = 1, c = 1
y = x² + x + 1 (upside)
If a = -1, b = 1, c = 1
y = -x² + x + 1 (downside)
Thus, the quadratic function, y = ax²+ bx + c opening upside if the value of 'a' is positive.
Learn more about quadratic equations here:
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What is 58 - 45.183?
Answer: 12.817
Step-by-step explanation: hope it helps! PLEASE SELECT ME BRAINLIEST!♡
If the sin 90 = 1 , then the cos 0 =
Rule of trigonometric functions:-
sin a = cos(90 - a)
Here a = 90°.
sin 90 = cos (90 - 90)
1 = cos 0.
cos 0 = 1.
So the cos 0 = 1.
Answer:
Step-by-step explanation:
If sin 90 = 1
then cos 0 will be
as we know that
cosx = sin(90-x)
If we plug x = 0 ,
cos0 = sin 90 = 1
Ann is grouping 38 rocks. She can put them into groups of 10 rocks or as single rocks. What are the different ways Ann can group the rocks?
Answer: There will be two different ways of doing so.
Step-by-step explanation:
Since we have given that
Total number of rocks =38
If we want to groups of 10 rocks or as single rocks then there are 2 different ways ;
Case I:
if we group into 10 rocks
there will be four sets in which Ist set contains 10 rocks
Second set contains 10 rocks
Third set contains 10 rocks
and Fourth set remains with 8 rocks only.
Case II:
if we group as single rocks .
There will be 38 sets .
Question 44 Unsaved
Find the measure of an angle between 0° and 360° coterminal with an angle of -271° in standard position.
Question 44 options:
181°
91°
271°
89°
Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.
Answer: 89°Coterminal angles are angles that have the same terminal sides in standard position.
Anytime we complete a full cycle( a complete revolution) we come back to the same terminal side.
Therefore to find all angles which are coterminal with [tex]-271\degree[/tex] we keep adding or subtracting [tex]360\degree[/tex].
For the given interval, that is, [tex]0\degree[/tex] to [tex]360\degree[/tex],
We add [tex]360\degree[/tex] so that we can obtain an angle coterminal with [tex]-271\degree[/tex] within this interval.
This means that
[tex]-271\degree[/tex] is coterminal with [tex]360\degree + \: -271\degree=89\degree[/tex]
Hence the correct and answer is D
Four girls helped Mr. Day plant a garden. For their help, he gave the girls $24 to share equally.later, mrs. day gave each girl $2 for helping to clean up. How much money did each girl get?
they all split it and is each going to have 6 dollars each plus the extra 2 for cleaning so 8 dollars each.
Answer - $8 Dollars
Each girl received a total of $8 after dividing the $24 from gardening equally among four girls and adding an extra $2 given by Mrs. Day for cleaning up.
The question asks how much money each girl received in total for helping with gardening and cleaning up. To find the answer, we first calculate how much each girl got from the $24 shared equally and then add the additional money each received from Mrs. Day.
Divide the $24 equally among the four girls: $24 \/ 4 = $6 per girl from gardening.Add the extra $2 each girl received for cleaning up: $6 (from gardening) + $2 (from cleanup) = $8 total per girl.Therefore, each girl received $8 in total from helping Mr. and Mrs. Day with gardening and cleaning up.
How many movies did Andrew rent this month if the month’s bill was $16.25
From my research i found the answer to be that he rented 9 movies.
Final answer:
To find out how many movies Andrew rented, subtract the membership fee from the total bill, then divide by the cost per movie. This reveals Andrew rented 9 movies.
Explanation:
To solve how many movies Andrew rented this month, we first need to subtract the monthly membership fee from the total bill. Knowing the monthly membership fee is $5.00 and the total bill was $16.25, we can calculate the cost of movies rented alone.
First, subtract the membership fee from the total bill: $16.25 - $5.00 = $11.25. This is the amount spent on renting movies.
Next, divide the result by the cost per movie, which is $1.25 per movie. This gives us: $11.25 / $1.25 = 9.
Therefore, Andrew rented 9 movies this month.
Factor. 25x^12-36y^14
The answer is: [tex](5x^{6}+6y^{7}) (5x^{6} - 6y^{7})[/tex]
To get answer: Factor [tex]25x^{12} -36y^{14}[/tex]
[tex]-36y^{14} +25x^{12}[/tex]
[tex]= (6y^{7} +5x^{6})(-6y^{7}+5x^{6})[/tex]
(5x⁶+6y⁷)×(5x⁶−6y⁷)
This is your answer hope this helps! Have a good day/night whatever time it is near you!
A married couple together earns 110,000 a year. The wife earns 16,000 less than twice what her husband earns.what does the husband earn
The husband earns $42,000 per year.
Let's denote the husband's earnings as H.
According to the problem, the wife earns 16,000 less than twice what her husband earns. So, the wife's earnings can be represented as (2H - 16,000).
We know that together they earn 110,000 per year. This can be written as:
H + (2H - 16,000) = 110,000
Combining like terms, this equation simplifies to:
3H - 16,000 = 110,000
Add 16,000 to both sides to solve for H:
3H = 126,000
Divide both sides by 3:
H = 42,000
Therefore, the husband earns $42,000 per year.
can somebody please help me with this problem thank you
After 5 months, they would both have the same cost. If you were to cancel after 9 months, you would cancel $320 for the first option and $360 for the second option.
To solve this, you need to create an equation. You get $50+30x and let x=number of months. This would tell you how much you need to pay for option 1. In option 2, you would have $40x. This is because there is no setup fee and so there would only be the monthly cost.We then set thos equations both equal to each other because the first question asks for the options to be the same price. For the second question, you would need to substitute 9 for the x in those equations. That would have you find out which is more expensive.
Find the product of x+4 and x²-2x-17 .
The buffalo bills scored 24 more than twice the number of points that the Miami dolphins scored. Altogether, the teams scored 66 points. How many did each team score individually?
Final answer:
The Miami Dolphins scored 14 points, while the Buffalo Bills scored 52 points, totaling 66 points as per the equation representing their scores.
Explanation:
Let's denote the number of points the Miami Dolphins scored as D. According to the question, the Buffalo Bills scored 24 more than twice the number of points that the Miami Dolphins did. This can be expressed as 2D + 24 for the Buffalo Bills' score. The total points scored by both teams is given as 66.
We can set up an equation to represent this situation:
D + (2D + 24) = 66
Simplify and solve for D:
Combine like terms: 3D + 24 = 66
Subtract 24 from both sides: 3D = 42
Divide both sides by 3: D = 14
So, the Miami Dolphins scored 14 points. We can then calculate the Buffalo Bills' score by plugging D into the Buffalo Bills' score equation:
2(14) + 24 = 28 + 24 = 52
Therefore, the Buffalo Bills scored 52 points.
In conclusion, the Miami Dolphins scored 14 points, and the Buffalo Bills scored 52 points.
write this number in expanded form 5,002,822
if you place 1 000.00 in a savings account with an interest rate of 3.25%/ month, how much should you earn in interest at the end of the month
A- $3.25
B-$32.50
C-325.00
D-$0.33
B is your answer.
(1000x0.0325)/100= 32.50.
Hope this helps & good luck. :)
Literal equations 5y-72=7+5x
Step 1. Add 72 to both sides
5y = 7 + 5x + 72
Step 2. Simplify 7 + 5x + 72 to 5x + 79
5y = 5x + 79
Step 3. Divide both sides by 5
y = 5x + 79/5
What’s the product of -3/4(-4)
The product is 3 because -3/4 * -4 is 3
Line segment CD is congruent to line segment XY. Which of the following is an equivalent statement?
Answer:
the answer is b
Step-by-step explanation:
solve sin(3x)=1/4 for all X, X in degrees
ANSWER
[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.
EXPLANATION
We want to solve the trigonometric equation;
[tex]Sin(3x)=\frac{1}{4}[/tex]
Since sine ratio is positive, it means the argument,[tex](3x)[/tex] is either the first quadrant or second quadrant.
This implies that;
[tex](3x)=arcsin(\frac{1}{4})[/tex]
[tex](3x)=14.5\degree[/tex] in the first quadrant.
Or
[tex](3x)=180\degree-14.5\degree=165.5\degree[/tex] in the second quadrant.
Since the sine function has a period of [tex]360\degree[/tex], The general solution is given by
[tex](3x)=14.5\degree+360\degree n\:or\:(3x)=165.5\degree +360\degree n[/tex],for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.
Dividing through by 3, we obtain the final solution to be;
[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.
Find the equation of the line which passes through the point (−3, 5) and is perpendicular to the line 4x + 3y = 6. Express your answer in slope-intercept form.
Answer:
[tex]y=\dfrac{3}{4}x+7\dfrac{1}{4}[/tex]
Step-by-step explanation:
[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1[/tex]
Let [tex]k:4x+3y=6\to 3y=-4x+6\ \ \ \ |:3\\\\y=-\dfrac{4}{3}x+2\\\\m_1=-\dfrac{4}{3}[/tex]
[tex]l:y=m_2x+b\\\\l\ \perp\ k\ \iff\ -\dfrac{4}{3}m_2=-1\qquad|\cdot\left(-\dfrac{3}{4}\right)\\\\m_2=\dfrac{3}{4}\\\\l:y=\dfrac{3}{4}x+b[/tex]
The line l passes through the point (-3, 5).
Substitute the coordinates of the point to the equation of the function l:
[tex]5=\dfrac{3}{4}(-3)+b\\\\5=-\dfrac{9}{4}+b\\\\5=-2\dfrac{1}{4}+b\qquad|+2\dfrac{1}{4}\\\\b=7\dfrac{1}{4}[/tex]
Finally [tex]l:y=\dfrac{3}{4}x+7\dfrac{1}{4}[/tex]
If the kite is 500 feet of string how high is it above the ground if the horizontal distance between Tyler and the kite is 300 feet
Pythagorean Theorem:
500^2 = 300^2 + x^2
250,000 = 90,000 + x^2
160,000 = x^2
x = +/- 400 use the positive root
height is 400ft
The kite is 400 feet above the ground.
To determine how high the kite is above the ground if it is 500 feet of string out and the horizontal distance between Tyler and the kite is 300 feet, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides).
In this scenario, imagine a right triangle where the string of the kite represents the hypotenuse, the horizontal distance from Tyler to the point directly underneath the kite represents the adjacent side, and the height of the kite above the ground represents the opposite side.
The length of the hypotenuse (the string) is given as 500 feet, and the length of the adjacent side (the horizontal distance) is 300 feet. To find the height of the kite (the opposite side), we apply the Pythagorean theorem:
[tex]\( c^2 = a^2 + b^2 \rightarrow 500^2 = 300^2 + b^2 \rightarrow 250000 = 90000 + b^2 \rightarrow \\b^2 = 250000 - 90000 \rightarrow b^2 = 160000 \rightarrow b = \sqrt{160000} \rightarrow b = 400 )[/tex]
Therefore, the height of the kite above the ground is 400 feet.
On Monday Leah ran 4.5 miles on Tuesday she ran 1-3 that distance what is the total distance she ran
Lolita reads 245 pages in 5 hours. How fast does she read?
she reads 49 pages in one hour.
The answer is 49 pages per hour
A movie theater sold 5 times as many children's tickets as adult tickets to an afternoon shoe. If 132 tickets were sold in all, how many were children's tickets
The 132 tickets is the childrens tickets and the adult tickets together. So to find the adult tickets you subtract the childrens tickets from the full amount. To find the amount of adult tickets you would take the group of adults which is '1' and the childrens tickets which is '5' so in total six. Then you will divide 132 by six and that should be 22.
in August Emily's clothing store sold 460 shirts with the ratio of short sleeve to long sleeve being 3:7. how many short sleeve shirts were sold
Answer: There are 138 short sleeves t-shirts.
Step-by-step explanation:
Given : In August Emily's clothing store sold 460 shirts with the ratio of short sleeve to long sleeve being 3:7.
Let the number of short sleeves shirts be 3x and the number of long sleeves shirts be 7x.
Then, according to the given question, we have
[tex]7x+3x=460\\\\\Rightarrow\ 10x=460\\\\\Rightarrow\ x=46[/tex]
Now, the number of short sleeves shirt = 3(46)=138
Hence , there are 138 short sleeves shirts.
Wjat is 6.05 in standard form
THIRTY POINTS ASAP!!!! when a number is multiplied by 6 the result is 3. find the number
x * 6 = 3
x = 3 : 6
x = 3/6
x = 1/2 or 0.5
A 100 pound person on earth would weigh about 4×4×4×4 pounds on Jupiter. Evaluate the expression to determine how much a 100 pound person would weigh on Jupiter. How much would a 200 pound person weigh?
That is 256
We get this by doing 4*4*4*4
so 4*4 is 16, then 16*4 is 64, then 64*4 is 256
So a 100lbs person would weigh 256 pounds on jupiter, or 4^4
Hello there,
Your correct answer is C your work is below
Ok so 4 to the 4th power is 256
we do this by multiplyg 4 times 4 times 4 times 4 and get 256
Also the exact weight of 200 pounds in jupiter is 510.40 and 512 is the nearest
If my answer helped please mark me as brainliest it would help thank you and have the best day ever!
In an election, everyone voted for either Cindy of Shawn. Cindy received 55% of the voters. Shawn received 423 votes. How many total people voted in the election?
Answer:
940 people
Step-by-step explanation:
since we know that 423 is 45% of the vote, we would do
45/100 =423/x, when you simplify the proportion, you find out that 940 people
In geometry, a solid may exist in three-dimensional space. A. True B. False
In geometry, a solid may exist in three-dimensional space is a TRUE statement.
Step-by-step explanation:In geometry, a solid shape is a three-dimensional figure which has width, depth and height.
Examples of such solids are:
Pyramid,cone, cubes etc.
The study of such solid shapes is known as a solid geometry.
Hence, the statement:
In geometry, a solid may exist in three-dimensional space is a TRUE statement.
The number of question on an exam varies with the number
Answer:
[tex]t=5x[/tex]
Step-by-step explanation:
So the number of questions in an exam varies with the number of minutes to take the exam.
For each question there are 5 minutes allotted.
Lets say that there are 'x' number of questions in the exam and 't' is the total time taken to finish the exam, in minutes. So the time taken to complete the exam would be
[tex]5 \times x=5x[/tex]
Therefore, the equation relating the time taken to complete the exam and the number of questions is given by:
[tex]t=5x[/tex]
So there are two variables in the equation, 't', and 'x':
t - time taken to complete the exam
x - number of questions on the exam