Formula: [tex]A=lw[/tex] where l is the length and w is the width
Whenever we modify any of the side lengths, as in make them longer or shorter, we simply add or subtract from l or w.
Standard FormWhen a quadratic equation is organized in standard form, it follows the following format:
[tex]y=ax^2+bx+c[/tex] where a, b and c are numbers
In standard form, all the terms have been simplified and there are no parentheses to expand.
Solving the QuestionWe're given:
Square garden has measurements of 10 ft by 10 ftWe're expanding each side by xWe must find the area of the garden in standard formIf we're expanding each side by x, we're simply adding x to each side length:
10 ft by 10 ft ⇒ (x + 10) ft by (x + 10) ft
Now to find the area, we can use the area formula:
[tex]A=(x+10)(x+10)[/tex]
This expression can be simplified as l = w:
[tex]A=(x+10)^2[/tex]
Putting it into standard form:
We can do this by expanding the parentheses:
[tex]A=(x+10)^2[/tex]
⇒ Because this is a perfect square, we can use the following rule to help us expand this equation:
[tex](a+b)^2=a^2+2ab+b^2[/tex][tex]A=x^2+20x+100[/tex]
AnswerTherefore, the expression in standard form that represents the area of the new expanded garden is [tex]x^2+20x+100[/tex].
Nina is older than Wayne but younger than Helen. Tony is older than Helen. Who is older, Tony or Wayne?
Answer:
tony
Step-by-step explanation:
tony is older than him
Which of the following describes the function shown in the table below? x y -4 16 -1 2 2 0. 25 4 0. 0625 5 0. 03125 exponential, there is a constant rate of growth exponential, there is a constant rate of decay or decrease quadratic, there is a second degree change in the y-values quadratic, there is a constant difference between consecutive y-values.
The given table is an example of constant exponential decay.
It is given that
X Y
-4 16
-1 2
2 0.25
4 0.0625
5 0.03125
What is an exponential function?An exponential function is a relation of the form y = a^x, with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
The y-value at -4 is 16 while the y-value at -1 is 2, a decrement of 1/8 times for an increment in x-value by 3
Again, the y-value at 2 is 0.25 while the y-value at 5 is 0.03125, a decrement of 1/8 times for an increment in x-value by 3.
In both cases, the rate of decrement is constant.
So we can say that this is an example of constant exponential decay.
We can also see this behavior from the attached graph.
Therefore, the given table is an example of constant exponential decay.
To get more about exponential function visit:
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there are 640 students in a school ,384 of them are boys.find the percentage of girls in the school.
Answer:
40%
Step-by-step explanation:
Given,
Total no.of students=640Number of boys=384Number of girls=Total no.of students - Number of boys=256Here,
Percentage of girls=256/640×100%
= 40%
F (x) = -x f(0) = ..............
Find value of x
Answer:
0
Step-by-step explanation:
Its equal to something multiplied by 0 so it is 0
Katarina bought a package of 500 stickers. Each sheet in the package has 20 stickers.
25% of the stickers on each sheet are hearts. The remaining stickers are stars.
Drag the tiles to identify the number of heart stickers and the number of star stickers in the package.
Numbers may be used once or not at all.
20
25
100
125
325
375
475
480
Number of Heart Stickers
Number of Star Stickers Pls tell me it really hard :(
Step-by-step explanation:
Total number of stickers is 500.
25% of the total number is hearts:
500*25/100 = 125 heart stickersThe rest of the stickers are stars:
500 - 125 = 375 star stickersWhat are all the real zeros of y=(x-20)^2 +5
Please show step by step I'm so lost!!
Answer:
No real zeros for the function.
Explanation:
zero of a function f, if f(r) = 0solve:
[tex]\sf y=(x-20)^2 +5[/tex]
so when f(y) = 0
[tex]\hookrightarrow \sf (x-20)^2 +5 = 0[/tex]
[tex]\hookrightarrow \sf (x-20)^2 = -5[/tex]
[tex]\hookrightarrow \sf (x-20) = \sqrt{-5}[/tex]
[tex]\hookrightarrow \sf x = \pm \sqrt{-5} +20[/tex]
[tex]\hookrightarrow \sf x = \sqrt{-5} +20, \ \sf x = -\sqrt{-5} +20[/tex]
check:
[tex]\hookrightarrow f \sf (\sqrt{-5} +20) = Not \ applicable[/tex], [tex]f \sf (-\sqrt{-5} +20) = Not \ applicable[/tex]
Answer:
No real zeros.
Step-by-step explanation:
Given... y = [tex](x-20)^{2} +5[/tex]
Since above equation has no real real value, there are no zeros.
But complex zeros are:
[tex](x-20)^{2} +5=0[/tex]
[tex](x-20)^{2} =-5[/tex]
I was late so mark the person above me Brainliest!
Mrs. alomry drives to school every day. today she has 5 gallons of gas in her car. the fuel warning light comes on if the amount of gas in the tank drops below 2 gallons. she uses about 1/2 gallon of gas per round trip. how many round trips can mr. alomry take before her warning light turns on.
Answer:
she can take six round trips before her warning light turns on
write an inequality that shows that vin total savings for the month are at least $100
Answer:
v >_100
Step-by-step explanation:
there is a line underneath the sign it won't let me write that so I just wanted to let u know.
A triangle has two angles that measure 85 and 23. Which has to be the measure of the third angle?
95
∘
72
∘
157
∘
Please help me please please please
Step-by-step explanation:
Given :-A triangle have two angles that measures 85° and 23°.To Find :-Measure of the third angle.Solution :-Let the measure of the third angle of the triangle be x.
As we know that,
The sum of all three sides of a triangle is 180° which is the angle sum property of triangle.Therefore,
[tex] \sf \longrightarrow {\angle{A}\ +\ \angle{B}\ +\ \angle{C}\ =\ 180^{\circ}} [/tex]
[tex] \sf \longrightarrow {85^{\circ}\ +\ 23^{\circ}\ +\ x\ =\ 180^{\circ}} [/tex]
[tex] \sf \longrightarrow {108^{\circ}\ +\ x\ =\ 180^{\circ}} [/tex]
[tex] \sf \longrightarrow {x\ =\ 180^{\circ}\ -\ 108^{\circ}} [/tex]
[tex] \bf \longrightarrow {\underline{x\ =\ 72^{\circ}}}\ \bigstar [/tex]
∴ Hence, the measure of the third angle of the triangle is 72°.
8. Jenny is getting dressed for school,
• She has 2 pairs of black pants, 1 pair of brown pants, and 2 pairs of blue pants in her
closet
. She also has 2 pink T-shirts and blue T-shirts in her closet.
• Without looking, Jonny pulls out one pair of pants and one T-shirt from her closet.
What is the probability that Jenny pulls out a pair of black pants and a blue T-shirt?
Answer:
[tex]\huge\boxed{\bf\: Probability = \frac{4}{9}}[/tex]
Step-by-step explanation:
According to the given information,
Pairs of black pants = 2Pair of brown pants = 1Pairs of blue pants = 2Then, total pairs of pants = 2 + 1 + 2 = 5
Similarly,
Pink T-shirts = 2Blue T-shirts = 2Then, total number of T-shirts = 4
This gives us the total nunber of clothing articles with Jenny, i.e.,
Total pairs of pants + Total number of T-shirts
= 5 + 4
= 9
Now, the probability of pulling out a pair of black pants & a blue T-shirt will be:
Total pairs of black pants + Total nunber of blue T-shirts/Total clothing articles
= 2 + 2 / 9
= 4/9
[tex]\rule{150}{2}[/tex]
help please im in class rn
Answer:
17 is the total perimeter of the shape on the perimeter grid
I need Help!!!
(Question is attached)
Answer:
SEE BELOW
Step-by-step explanation:
1 - 12000 ft
2 - 10 minutes
3 - The third segment in he graph is not as steep as the first segment because the flight took more time to lose altitude than the time taken to gain altitude.
Hope it helped
PLEASE HELP ME ((UNIT RATES)) 20 points again, brainliest will be given.
I think the answer is A sorry if it's wrong
12(x+3y-6z)
please expand the answer!!!!
6. [tex]4(-8a-5b+3) = -32a-20b+12 = 12-32a-20b\\[/tex]
8. [tex]12(x+3y-6z) = 12x+36y-72z[/tex]
Hope that helped!
HELP I NEED THIS FOR TODAY!! 100 points
Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −3x2 + 24x + 3 and y = −4x2 + 25x + 15, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?
3.25 seconds
3.50 seconds
3.75 seconds
4.00 seconds
What are the solutions to the following system of equations?
x − y = 6
y = x2 −6
(0, −6) and (7, 1)
(0, −6) and (1, −5)
(0, −6) and (9, 3)
(0, −6) and (−9, 3)
Based on the graphs of the equations y = x + 7 and y = x2 – 3x + 7, the solutions are located at points:
(4, 11) and (0, 7)
(4, 11) and (–7, 0)
(–7, 0) and (1.5, 4.75)
(1.5, 4.75) and (0, 7)
Which system of equations is represented by the graph?
Graph of a quadratic function intersecting a linear function at point 2 comma 0.
y = x2 + 3x + 2
x + y = 2
y = x2 − 3x + 2
x − y = 2
y = x2 − 3x + 2
x − y = 3
y = x2 − 3x + 2
x + y = 3
The solutions of the given equations are given by equating the
variables to gives;
First part; 4.00 secondsSecond part; (0, -6) and (1, -5)Third part; (4, 11) and (0, 7)Fourth part: y = x² + 3·x + 2; x + y = 2How can the (common) solution be found?First part;
The given functions are;
y = -3·x² + 24·x + 3, and y = -4·x² + 25·x + 15
When the balloons collided, we have;
The height are equal, which gives;
y = y
-3·x² + 24·x + 3 = -4·x² + 25·x + 15
-3·x² + 24·x + 3 - (-4·x² + 25·x + 15) = x² - x - 12 = 0
Which gives;
x² - x - 12 = (x - 4) × (x + 3) = 0
x = 4, and x = -3
The time at which the balloon collide at the highest point is therefore;
At the time, x = 4.00 secondsSecond part;
The given system of equations are;
x - y = 6
y = x² - 6
y = x - 6
Which gives;
x - 6 = x² - 6
x = x²
Which gives;
x = 0 or x = 1
Similarly, we have;
x = y + 6
Which gives;
y = (y + 6)² - 6
y² + 11·y + 30 = 0
(y + 5)·(y + 6) = 0
Which gives;
y = -5, or y = -6
When y = -5, we have; x = -5 + 6 = 1
The solution are therefore;
(0, -6) and (1, -5)Third part;
The equations are; y = x + 7 and y = x² - 3·x + 7
At the solution, the u-values are equal, which gives;
y = y
x + 7 = x² - 3·x + 7
x² - 3·x + 7 - (x + 7) = 0
x² - 4·x = 0
x·(x - 4) = 0
x = 4, or x = 0
When x = 4, y = 4 + 7 = 11
When x = 0, y = 0 + 7 = 7
The solutions are located at points;
(4, 11) and (0, 7)Fourth part;
Given that the point of intersection of the line and the quadratic function
is the point (2, 0), we have;
On the linear function, when y = 0, x = 2
The possible linear function functions is therefore;
x + y = 2
From the quadratic function that accompanies the above linear function, we have;
y = x² + 3·x + 2
When x = 0, y = 0² + 3×0 + 2 = 2
Therefore;
The correct option is; y = x² + 3·x + 2, and x + y = 2Learn more about the solutions of equations here:
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WILL GIVE BRAINLIEST IF CORRECT PLEASE ANSWER!!!!!!
Solve for x. Round to the nearest tenth, if necessary.
Answer: 20.4
Step-by-step explanation: U = 74°
Cos 74 = x/74
x = 74 * Cos 74
x = 20.39716433 or 20.4
A recent survey of 8,000 high school students found that the mean price of a prom dress was $195. 00 with a standard deviation of $12. 0. Alyssa thinks that her school is more fashion conscious and that students spent more than $195. 0. She collected data from 20 people in her high school and found that the average price spent on a prom dress was $208. 0. Which of the following are the correct null hypothesis and alternate hypothesis? H0: Mu = 195; Ha: Mu greater-than 195 H0: Mu not-equals 195; Ha: Mu = 208 H0: Mu = 195; Ha: Mu not-equals 195 H0: Mu = 195; Ha: Mu greater-than-or-equal-to 208.
The correct null hypothesis and alternate hypothesis will be
[tex]H_{0} =\mu=195\\H_{a} =\mu > 195[/tex]
What will be the correct null hypothesis and alternate hypothesis?It is given that
The mean price of a prom dress was $195. 00 with a standard deviation of $12. 0
Given that Alyssa thinks that her school is more fashion-conscious and that students spent more than $195.00.
She collected data from 20 people in her high school and found that the average price spent on a prom dress was $208.00.
Since she wants to check whether the sample mean [tex]\mu[/tex] is the same as the population mean [tex]\mu[/tex] = 195
[tex]H_{0} =\mu=195\\H_{a} =\mu > 195[/tex]
(Right hypothesis test)
Thus the correct null hypothesis and alternate hypothesis will be
[tex]H_{0} =\mu=195\\H_{a} =\mu > 195[/tex]
To learn more about null hypotheses follow
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Answer: OPTION A
Step-by-step explanation:
Plssss help if you know how to do it Plss
yes they are similar, one is 3/4ths of the other for all dimensions if you match it up right
Which points have the coordinates (−212,0.5) , (2,512) , and (3.5,−412) on the coordinate plane?
Answer:
A: (-2.12, 0.5)
D: (2, 5.12)
E: (3.5, -4.12)
I'm going to assume that the three digit numbers have a decimal :))
Bryan's volunteer group can build a garage in 12 hours. When he works with Sequoia's volunteer
group, it takes 4 hours to build the garage together. How long does it take Sequoia's volunteer
group to build the garage alone? (Do not include the units in your answer. )
Answer:
Step-by-step explanation:
Known:
A fraction represents a part of a whole or, more generally, any number of equal parts.Given:
The volunteer group can build a garage in 12 hours. Sequoia's group can build it inTo find:
The Bryan's long would it take them if they worked together.Brian's group ⇒ 1 garage in 12 hours ( [tex]\frac{1garage}{12hours}[/tex])
Sequoia's group ⇒ 1 garage in 16 hours ([tex]\frac{1garage}{16hours\\}[/tex])
To make it easier to calculate the time it would take if they worked together, we will write this expression:
[tex]\frac{1}{12} +\frac{1}{16} =\frac{4}{48} +\frac{3}{48} =\frac{7}{48} \\[/tex]
From this fraction we see that for 7 garages they would need 48 hours. . To calculate how much time they would need for
1 garage, we will further simplify the fraction.
Solving the worked together is would need
6.86 hours for one garage.
Flag question: Question 1
Question 14 pts
Is this ordered pair a solution for the equation?
(4, 11)
y = x + 7
Group of answer choices
True
False
answer
False
the x and y of Y=x+7 is x=-7 and y=7 not 100% sure pls someone recheck
What is the earliest known reference to pi in history.
Answer:
im sorry i dont know what is the history
Geet sells televisions. He earns a fixed amount for each television and an additional $15 if the buyer gets an extended warranty. If Geet sells 13 televisions with extended warranties, he earns $845. How much is the fixed amount Geet earns for each television?
The fixed amount Geet earns for each television he sells is $ .
Answer: The fixed amount Geet earns for each television is $60.
Step-by-step explanation: Geet sells televisions. He earns a fixed amount for each television and an additional $ 30 if the buyer gets an extended warranty. If Geet sells 17 televisions with extended warranties, he earns $ 1,530.Now, to find the fixed amount Geet earns for each television.Let the cost of fixed amount be .Number of television = 17.He earns total = $1,530.He earns additional amount = $30.Now, to get the fixed amount we put an equation: Subtracting both sides by 510 we get:Dividing both sides by 17 we get:Therefore, the fixed amount Geet earns for each television is $60.
Answer:
$15 Fixed Amount Per TV
Step-by-step explanation:
13 x 15 = 195 - Extended Warranty
845 - 195 = 650
650 ÷ 13 = 50 - Fixed Amount
what is the area for this shape
Answer:
area = 697.5 ft²
Step-by-step explanation:
Think of an outer large rectangle minus a smaller upper rectangle.
area = LW - lw
area = (45 ft)(20 ft) - (45 ft - 10 ft - 8 ft)(7.5 ft)
area = 900 ft² - (27 ft)(7.5 ft)
area = 900 ft² - 202.5 ft²
area = 697.5 ft²
Evaluate (15 – 4x) + 5 when x = 3.
First, evaluate within the parentheses. Then evaluate exponents. Next multiply and divide from left to right. Then, add and subtract from left to right.
Complete the statements.
Substitute the given value for the .
Use the to simplify.
First, complete the inside the parentheses.
Next, complete the inside the parentheses.
Last, complete the addition.
The value is .
Vijay bought a camera that was marked down 80% from an original price of $355. If he paid 4% sales tax, what was the total cost of the camera?
Answer:
answer is 266
Step-by-step explanation:
80% of 355 is 280
4% of 355 is 14
280-14=266
If DF=7x-3 and EG=5x+9, find the value of X
Answer:
6[tex] \: [/tex]
Step-by-step explanation:
A rectangle is a parallelogram with equal angles and the diagonals of a rectangle are of equal length.
[tex] \: [/tex]
Therefore,
[tex]\\ { \longrightarrow \qquad{ \sf{ \pmb {DF = EG}}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \pmb {7x - 3 = 5x + 9}}}} \: \: \\ \\[/tex]
Subtracting 5x from both sides we get :
[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {7x - 5x - 3 = 5x - 5x + 9}}}} \: \: \\ \\[/tex]
[tex] { \longrightarrow \qquad{ \sf{ \pmb {2x - 3 = 9}}}} \: \: \\ \\[/tex]
Adding 3 to both sides we get :
[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {2x - 3 + 3 = 9 + 3}}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x = 12}}}} \: \: \\ \\[/tex]
Dividing 2 from both sides we get :
[tex]\\ { \longrightarrow \qquad{ \sf{ \pmb { \frac{2x}{2} = \frac{12}{2} }}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \frak{ \pmb {x = 6}}}} \: \: \\ \\[/tex]
Therefore,
The value of x is 6Line l is perpendicular to line m. What are the values of angles x and w?Enter your answers in the boxes below
Answer:
Step-by-step explanation:
I need a graph. but from what you're telling me they are both 90 degrees
i need help please (algebra 1)
Answer :
Option C (x = 3 or x = -13)⠀
Explanation :
⠀
[tex] \longrightarrow \sf \qquad {x}^{2} + 10x = 39[/tex]
⠀
We can write it as,
[tex] \longrightarrow \sf \qquad {x}^{2} + 10x - 39 = 0[/tex]
⠀
We have to find the two numbers a and b such that,
[tex] \longrightarrow \sf \qquad a + b = 10[/tex]
[tex] \longrightarrow \sf \qquad a b = 39[/tex]
⠀
Obviously, the two numbers are 3 and 13.
[tex] \longrightarrow \sf \qquad {x}^{2} - 3x + 13x - 39 = 0[/tex]
[tex]\longrightarrow \sf \qquad {x}(x - 3)+ 13(x - 3) = 0[/tex]
[tex]\longrightarrow \sf \qquad ({x}+ 13)(x - 3) = 0[/tex]
⠀
Whether, the value of x :
[tex]\longrightarrow \sf \qquad {x}+ 13 = 0[/tex]
[tex]\longrightarrow \pmb{\bf \qquad {x} = - 13}[/tex]
⠀
Whether, the value of x :
[tex]\longrightarrow \sf \qquad {x} - 3 = 0[/tex]
[tex]{\longrightarrow { \pmb{\bf \qquad {x} = 3}}}[/tex]
⠀
So,
Option C (x = 3 or x = -13) is correct.What is the equation of a circle with center (-3, -5) and radius 4?
Answer:
[tex](x+3)^{2} +(y+5)^{2} =16[/tex]
Step-by-step explanation:
the general equation of a circle is
[tex](x-h)^{2} + (y-k)^{2} =r^{2}[/tex]
with (h,k) being the centre of the circle and r the radius