Step-by-step explanation:
We know the quadratic formula, which is :
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}} \\ \\ [/tex]
Here,
a = 1b = -6c = -5So,
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - ( - 6) \pm \sqrt{ {( - 6)}^{2} - 4(1)( - 5) } }{2(1)} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 - 4( - 5) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 + 20 } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 56 } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(28) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(14) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(2)(7) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2} . \sqrt{2} . \sqrt{2 . 7} }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
Now, Separating the solutions :
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 + 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = 3 + \sqrt{14}}}}\\ \\ [/tex]
[tex]\\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 - 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = 3 - \sqrt{14}}}}\\ \\ [/tex]
Math question! Please help! 100 points
An arithmetic sequence has first term a = 5 and common difference d = 2. How many terms of this sequence must be added to get 1440?
To find how many terms of this sequence must be added to get 1440, we must know the arithmetic sequence equation to find any term in the sequence:
⇒ [tex]a_{n}=a_{1} +(n-1)d[/tex]
[tex]a_{n}[/tex] --> value of the nth number of the sequence[tex]a_{1}[/tex] --> first term of the sequencen --> position of the nth termd --> common differenceLet's examine the information given:
first term a = 5⇒ [tex]a_{1} =5[/tex]
common difference d = 2⇒ d = 2
Therefore the equation for finding the nth term of the sequence so far is:
[tex]a_{n}=5+(n-1)*2=5+2n-2=3+2n[/tex]
Now we want to find how many terms this sequence must be added to get 1440
General equation for adding all the terms = [tex]\frac{n(a_{1}+a_{n} ) }{2}[/tex]
[tex]a_{1}[/tex]: first term of the sequence[tex]a_{n}[/tex]: last term of the sequencen: number of terms in the sequence.Using all the information given, let's plug in the all the values:
[tex]1440=\frac{n*(5+(3+2n))}{2} \\1440=\frac{n*(8+2n)}{2} \\2880=8n+2n^2\\2n^2+8n-2880=0\\(2n+80)(n-36)=0[/tex]
To solve this we set (2n + 80) = 0 and (n-36) = 0
[tex]2n+80=0\\ 2n = -80\\n= -40[/tex] [tex]n - 36 =0\\n = 36[/tex]
In this case, n can only equal 36 since n cannot be negative.
Answer: 36 terms of this sequence must be added to get 1440.
Hope that helps!
General formula
a_n=a+(n-1)ds_n=n/2[2a+(n-1)dWe need n
n/2[2(5)+2(n-1)]=1440n[10+2n-2]=2880n[2n+8]=28802n²+8n-2880=0n²+4n-1440=0(n+40)(n-36)=0Take it positive
n=36Which is the last operation when evaluating
subtraction [BODMAS 'S' comes last which means subtraction]
hope it helps...
Answer:
Subtraction
Step-by-step explanation:
Learn with an example
04
Watch a tutorial
Brooke has $7 in an account that earns 10% interest compounded annually.
To the nearest cent, how much will she have in 2 years?
Assuming that no transaction happens in her account for those 2 years, the amount that Brooke will have in 2 years for given case is $8.47
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We're specified that:
Initial amount in bank of Brooke = p = $7Interest rate = r = 10% = 0.10 (in decimal form), compounding annually.Due to annual appliance of the interest, we have n = 1The time for which this compounding will be done is t = 2 years.Thus, we get the final amount's value (after 2 years of compounding) for this case as :
[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 7(1 + 0.10)^2 = 7 \times (1.1)^2 = 7 \times 1.21 = 8.47 \: (\rm in \: dollars)[/tex]
Thus, assuming that no transaction happens in her account for those 2 years, the amount that Brooke will have in 2 years for given case is $8.47
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And buys six bags of apples each bag has eight apples if she shares the apples equally among her 12 soccer teammates how many apples will each teammate receive
Answer:
3
Step-by-step explanation:
What is the difference in length between the girls with the shortest and longest hair
Answer:
I think the difference is girls with longer hair look more attractive.
Step-by-step explanation:
Need the diagram....
Functions pls help will give brainlest
Answer:
See below
Step-by-step explanation:
1) put in -6 where 'x' is to get y = 7
2) There is only one value of 'y' for every value of 'x' <===function
3) Put in 2 where 'x' is to get y = 20
4) Function
What is the unknown fraction?
three tenths plus blank equals sixty one hundredths
A. thirty one hundredths
B. fifty eight hundredths
C. sixty four hundredths
D. one hundred and twenty two hundredths
Answer:
A. 31/100
Step-by-step explanation:
Change 3/10 to hundreds:
3/10 × 10/10 = 30/100
The denominator (the bottom number) must be 100.
61 - 30 is 31.
The missing number is 31/100. See image.
A basketball player shoots a free throw, where the position of the ball is modeled by x = (24cos 48°)t and y = 6.1 + (24sin 48°)t − 16t 2. What is the height of the ball, in feet, when it is 13 feet from the free throw line? Round to three decimal places.
I know how to do this but I keep getting a negative answer, is there an error with the question or am I just doing it wrong
Maybe ur just not seeing the negative comment on this and tell me which way u are solving it and then i can help.
The height of the ball is 10.053 approx. when it is 13 feet from the free throw line .
What is free throw?
The physics aspect of shooting a free throw involves distance and deviation. Distance is determined by two factors: launch angle and launch speed. Players have a choice between shooting for a larger target by using more arc or going for a shooter's touch and shooting with their ideal arc for their height.
According to the question
A basketball player shoots a free throw, where the position of the ball is modeled
x = (24cos 48°)t
y = 6.1 + (24sin 48°)t − [tex]16t^{2}[/tex]
now
13 feet from the free throw line
x = 13 feet (horizontal distance)
x = (24cos 48°)t
(24cos 48°)t = 13
t ≈ 0.8059
putting values in y to get the vertical height
y = 6.1 + (24sin 48°)t − [tex]16t^{2}[/tex]
y = 6.1 + (24sin 48°)*0.8059 − [tex]16*( 0.8059)^{2}[/tex]
y ≈ 10.053
Hence, the height of the ball is 10.053 approx.
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What is the reclusive rule for this geometric sequence? -64, -16, -4, -1
Answer:
See below ~
Step-by-step explanation:
Finding the common ratio (r)
Divide a term by the term precedes (follows) itr = -16/-64r = 1/4r = 0.25 [Blank 1 answer]First term (a₁)
The first term in the sequence is the term from which the sequence startsa₁ = -64 [Blank 2 answer]Tara is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 15 inches × 12
1
3
inches. She needs to cut another rectangle that is 10
1
2
inches by 10
1
3
inches. How many total square inches of construction paper does Tara need for her project
Answer:
280 Square Inches
Step-by-step explanation:
This problem is formatted quited weirdley, but Im giving my best hand forward to solve it.
We are given 2 rectangular fingures, and we need to figure out the total area Tara requires for her project.
When approaching these problems I preferably like to form equations.
Area of Rectangle 1 + Area of Rectangle 2 = Total Area
Now we plug in the values
(15x12) + (10x10) = T
180 + 100 = T
280 = T
What is the area of a rectangle with a length of 6 2/5 centimeters and a width of 2 3/5 centimeters?
Answer: [tex]16\frac{16}{25} cm^2[/tex]
Step-by-step explanation:
The formula for area is length × width = area
Sub in the values for length and width to solve
[tex]6\frac{2}{5}[/tex]×[tex]2\frac{3}{5}[/tex]=[tex]16\frac{16}{25}[/tex]
Find the measure of angle geh
Answer:
Hello there buddy I’m here too help you with your homework
Your answer is
110°
Hope it’s helps you buddy
Have a nice day
Good luck with your homework
Step-by-step explanation:
~FluffyZaynBerry
Simplify. 24a7 -8a5
Answer: 8a^5 (3a^2 - 1)
Step-by-step explanation:
I factored 8a^5 out of the 24a^7 - 8a^5
Find the point at which the line f ( x ) = − 4 x − 2 intersects the line g ( x ) = − x − 2
Answer:
Step-by-step explanation:
f(x) = - 4x - 2
g(x) = - x - 2
y-intercept is common point for both equations ( 0 , - 2 )
the difference between two numbers is 9. Find the numbers if their sum is 46
Answer:
[tex](\frac{55}{2} ,\frac{37}{2} )[/tex]
Step-by-step explanation:
We have to solve this system of equations in order to find the numbers :
Let x be greater number and y be the smaller one :
[tex]\begin{cases}x-y=9\ \ \ (1)&\\ x+y=46\ \ \ (2)&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=x-9\ \ \ (1)&\\ 2x=9+46=55\ \ \ (1)+(2)&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=\frac{55}{2} -9=\frac{37}{2} &\\ x=\frac{55}{2}&\end{cases}[/tex]
help pls i dont undestand it can you help thanks
3.8/24 is 0.1407
to get to a percentage you x100
so the answer is 14.07%
Follow the rules to create two number sequences that go to the fifth term each. Rule 1: Multiply by 2 starting at 10. Rule 2: Subtract 4 starting from 24. What is the first term that appears in both sequences? (2 points) Group of answer choices 10 14 20 26
Answer:
Step-by-step explanation:
Created Sequences
S1: 10 20 40 80 150
s2:24 20
The first term that appears in both sequences is the second term. Both of them equal 20.
I don't think you have to go any further once you get the first term.
Method
S1: Multiply by 2 starting with 10.
10*2 = 20
20*2 = 40
S2: Start at 24 and subtract 4
24 - 4 = 20
20 - 4 = 16
16 - 4 = 12
Classify the pairs of angles shown. Then find the value of X in each figure
The value of x in each figure is 34°, 17.1° and 75° respectively.
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
From the diagram:
1) x + 146° = 180° (sum of angles in a straight line)
x = 34°
2) x + 62.9° = 90° (complementary angles)
x = 17.1°
3) x + 105° = 180° (sum of angles in a straight line)
x = 75°
The value of x in each figure is 34°, 17.1° and 75° respectively.
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simply the square roots without using decimals
Answer:
The answer to the question√3
∠3 and ∠6 are _____________ because they are _______________________.
a supplementary/same-side interior angles
b supplementary/corresponding angles
c congruent/same-side interior angles
d congruent/corresponding angles
Answer: Option (1)
Step-by-step explanation:
∠3 and ∠6 are supplementary because they are same-side interior angles. Therefore, the correct answer is option A.
From the given figure, m and n are parallel lines and l is transversal.
Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
Here, angle 3 and angle 6 are co-interior angles and sum of their angles is supplementary.
Therefore, the correct answer is option A.
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what is the equation of a circle with center at (3,-4) and radius of 3
Answer:
[tex]\displaystyle [x - 3]^2 + [y + 4]^2 = 9[/tex]
Explanation:
Accourding to one of the circle equations, [tex]\displaystyle [x - h]^2 + [y - k]^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle [h, k].[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared.
I am joyous to assist you at any time.
Please answer!!!!! What is the probability that the dart will NOT land in the shades region?
Answer:
The answer is 25% also twenty five percent
BRAINLIEST!!!!! FAST ANSWER
The coordinate grid shown
represents a map of a park. A
portion of the park is going to be
upgraded with new playground
equipment and flowers
Part A
The portion of the park that is to
receive upgrades has the
following coordinates:
Part B
How much area, in square yards, will receive upgrades?
Part C
How much area, in square yards, will have red flowers?
Select locations of points
• Point A (-4,4)
• Point B (3, 4)
• Point C (3,-2)
• Point D (-4,-2)
Use the Add Point and Connect
Line tools to create the rectangle
ABCD.
Answer:
Part B : 42
Part C : 7
Step-by-step explanation:
After putting in the coordinate points the width of the rectangle is 7 units and the length is 6 units. 7*6 =42. Half of this is the area of the triangle, that is 21. Further , 1/3 of 21 is the same as 21 divided by 3, which equals 7.
Katie and her brother are both writing a report. Katie wrote 7/8 of her report. and her brother 3/7 of his report. What is the best estimate of how much more Katie wrote than her brother?
Answer:
Katie has successfully completed 7/8 of her report
HELP ME PLEASE!!
Find the length of segment SV.
A)
13/2
B)
26
C)
5.2
13
D)
V2
Applying the sine ratio, the length of segment SV (opposite side) in the right triangle is: D. 13/√2
What is the Sine Ratio?The sine ratio is used to solve a right triangle which is, sin θ = opp/hyp.
Given the following:
SU = 13 (hypotenuse)
θ = 45
SV = ? (opposite)
Note: sine 45 = 1/√2
Applying the sine ratio, we have:
sin 45 = SV/13
SV = sin 45 × 13
SV = 1/√2 × 13
SV = 13/√2
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he figure shows a parallelogram inside a rectangle outline:
A parallelogram is shown within a rectangle. The length of the rectangle is 3 over 5 foot, and the width of the rectangle is 2 over 5 foot. The two equal bases of the triangles outside the parallelogram are labeled 1 over 5 foot.
What is the area of the parallelogram?
1 over 25 square foot
11 over 25 square foot
3 over 25 square foot
4 over 25 square foot
Answer:
4/25 foot²
Step-by-step explanation:
Refer to attachment*
Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having
[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{2}{5}\times \dfrac25}[/tex]
[tex]{:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}[/tex]
Hence, Option D) is correct
Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have
[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\bigg(\dfrac{2}{5}\times \dfrac{3}{5}\bigg)-\bigg(\dfrac{1}{5}\times \dfrac{2}{5}\bigg)}[/tex]
[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{6}{25}-\dfrac{2}{25}}[/tex]
[tex]{:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}[/tex]
This also, proves that the correct answer is D)
find the circumference of the circle whose diameter is 14 cm
Circumference of the circle with diameter 14 cm is 43.96 cm.
What is the circumference?Circumference of any shape or figure is the total length of it's boundary. Circumference of a shape is also called the perimeter.
Circumference of any shape can be calculated by opening that shape into a straight line and then measuring the length of the line.
Perimeter of the circle can be computed by the formula,
C = 2πr, where r is the radius of the circle.
So, diameter of the circle is 2r
Here, we have, diameter = 2r = 14 cm
∴Circumference = 14π = 43.96 cm
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Emanuel needs 6 lengths of ribbon, each 4 feet long, to make ribbon flowers How much ribbon does he need altogether? Please Help
Answer:
24 feet
Step-by-step explanation:
Given
Length of a ribbon = 4 feetSolving
Length of 6 ribbons = Length of a ribbon x 64 feet x 624 feetWhich expression is equivalent to 6f+f?
Answer:
A
Step-by-step explanation:
This is because 6f+f is just 7f.
f f f f f f+f = fffffff
Soooo, ONLY A gives us 7f when added together again.
f+5f+f=7f.
f+ f f f f f +f = fffffff
Answer:
[tex]f + 5f + f[/tex] is equivalent to [tex]6f + f[/tex].
Step-by-step explanation:
You can plug in any numbers to both expressions and they will always have the same outcome.
For example, let's plug in 2.
[tex]6f + f\\6(2) + 2\\12 + 2 = 14[/tex]
[tex]f + 5f + f\\2 + 5(2) + 2\\2+10+2 = 14[/tex]
Hope this helps! :)
Find the tangents of the acute angles in the right triangle. Write each answer as a fraction.
tan J=
tan K=
Applying the tangent ratio, the tangents of the acute angles in the right triangle are:
tan J = 5/3
tan K = 3/5
What is the Tangent Ratio?The tangent ratio is used to find the tangents of an angle in a right triangle, or any of the legs. It is given as tan ∅ = opposite/adjacent.
Applying the tangents ratio:
tan J = opp/adj = 5/3
tan K = opp/adj = 3/5
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