Answer:
[tex]\dfrac12 < p < 5[/tex]
Step-by-step explanation:
To solve this, we need to use the discriminant.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
If the given equation has 2 real roots, then we need to use:
[tex]b^2-4ac > 0[/tex]
Given equation: [tex]8x^2-4x+1-p=0[/tex]
[tex]\implies a=8, \quad b=-4, \quad c=(1-p)[/tex]
Substituting these values into [tex]b^2-4ac > 0[/tex] and solve for p:
[tex]\implies (-4)^2-4(8)(1-p) > 0[/tex]
[tex]\implies 16-32(1-p) > 0[/tex]
[tex]\implies 16-32+32p > 0[/tex]
[tex]\implies -16+32p > 0[/tex]
[tex]\implies 32p > 16[/tex]
[tex]\implies p > \dfrac{16}{32}[/tex]
[tex]\implies p > \dfrac12[/tex]
For the roots to be less than 1, first find the value of p when the root is 1.
If the root is 1, then [tex](x-1)[/tex] will be a factor, so [tex]f(1)=0[/tex]
Substitute [tex]x=1[/tex] into the given equation and solve for p:
[tex]\implies 8(1)^2-4(1)+1-p=0[/tex]
[tex]\implies 5-p=0[/tex]
[tex]\implies p=5[/tex]
Therefore, the values of p for which the given equation has two different real roots less than 1 are:
[tex]\dfrac12 < p < 5[/tex]
What is the equation in standard
form of a circle with the
equation x^2+ y^2 + 14y – 1 = 0?
Answer:
(x-2)²+(y+7)² = 25Step-by-step explanation:
The general standard form of an equation is written in expressed as shown;
(x-a)²+(y-b)² = r²
(a,b) is the centre of the circle and r is the radius
Given the equation of the circle x^2 + y^2 - 4x + 14y +28 =0, we need to find the centre of the circle and its radius.
comparing the equation given with x²+y²+2gx+2fy+c =0
(-g, -f) is the centre
radius = √g²+f²-c
On comparison,
2gx = - 4x
g = -4/2
g = -2
2fy = 14y
f = 14/2
f = 7
c = 28
r = √(-2)²+7²-28
r = √4+49-28
r = √25
r = 5
comparing centre (a,b) to (-g, -f)
a = -g = -(-2)
a = 2
b = -f = -7
b = -7
substituting the centre (a, b) and the radius r into the equation
(x-a)²+(y-b)² = r²
The required equation will be (x-2)²+(y+7)² = 5²
(x-2)²+(y+7)² = 25
-y + 2y = what ? Please help and why is it negative or positive ?
Step-by-step explanation:
-y is the same as writing -1y. if we forget about the y’s, -1 + 2 = 1. so -1y + 2y = 1y, or just y to be simpler :)
i hope this helps :)
[tex]-y+2y=2y-y=(2-1)y=y[/tex]
It is positive because the coefficient is positive.
Find the value of b,c, and d.
Answer:
b = 25 degrees
c = 81 degrees
d = 64 degrees
Draw a box between the
A. minimum; maximum
B. first quartile; third quartile
C. second quartile; third quartile
D. first quartile; second quartile
and
Draw a box between the first quartile; third quartile
Can someone please show step by step to this problem? Find the area of the following figure.
Answer:
20 x 12=240
Step-by-step explanation:
What is the equation of this line in slope-intercept form?
y= 3x-1
y = 3x+1
y= - 1/3x-1
y = - 3x-1
Answer:
Step-by-step explanation:
y=-3x-1
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Recall: SOHCAHTOA
Sin M = Opp/Hyp
Reference angle = M
Opp = 3√/21
Hyp = 15
Sin M = (3-√21)/15
Sin M = √21/5
Cos M = Adj/Hyp
Reference angle = M
Adj = 6
Hyp = 15
Cos M = 6/15
Cos M = 2/5
Tan M = Opp/Adj
Reference angle = M
Opp = 3√21
Adj = 6
Tan M = (3√21)/6
Tan M = √21/2
:Therefore: Sin M = √21/5
Cos M = 2/5
Tan M = √21/2
Answer:
[tex]\sf \sin M=\boxed{\dfrac{\sqrt{21}}{5}}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = MO = 3√21A = 6H = 15[tex]\sf \sin M=\dfrac{3\sqrt{21}}{15}\quad\cos M=\dfrac{6}{15}\quad\tan M=\dfrac{3\sqrt{21}}{6}[/tex]
[tex]\implies \sf \sin M=\dfrac{3\sqrt{21}}{15}=\dfrac{\sqrt{21}}{5}[/tex]
Given two side lengths of a triangle (4cm and 17cm), find a range of possible lengths for the third side.
Check the picture below.
so notice the top part of the picture
if we move the "4" and "17" sides close to each other, till one is on top of the other, the side in red, can never be less than 17 - 4, or 13, it cannot be 13 either, because then both lines will be on on top and we wouldn't have a triangle just a flat-line, so whatever the red line is, it must be more than 13.
notice the bottom part of the picture
if we separate the "4" and "17" sides, and lay them flat, the most the red side can be is 4 + 17 or 21, it can never be greater than 21, it can't be 21 either because if we lay "4" and "17" flat, we lose the triangle and all we'd have is a flat-line. So whatever the red side is, must be less than 21.
standard form of 2⋅3⋅7⋅q⋅t
Answer:
42qt
Step-by-step explanation:
First, multiply 2 x 3 x 7
2 x 3 = 6
6 x 7 = 42
Second, q x t
Qt
Third, put together
42qt
what is 7/8 - 1/2 = in simplest form
Answer:
[tex] \frac{7}{8} - \frac{1}{2} = \frac{7 - 4}{8} = \frac{3}{8} [/tex]
Step-by-step explanation:
I hope I helped you! :)
Please solve the following thank you so much math experts
Answer:
4) 97%
6) 13%
Step-by-step explanation:
4) We are given that 3% for 250 million are diesel.
100% - 3% = 97% NON DIESEL cars
97% of 250 million is 242.45 million.
______________________________
6) We know that 17% (buses) and 70% (cars) are part of that total.
We also know that the total needs to be 100%
So, we simply do this:
100 - (17+70) = 13 (%)
So, 13% of the survey participants had bikes
I just made a purchase of $130.00 but once I got my car and looked at the receipt, I realized the salesperson who helped me did not apply the 15% discount
Answer:
Guessing you want me to figure out what your cost should have been. On it!
Step-by-step explanation:
130 * .15 = 19.5
130 - 19.5 = $110.5
That should be the new cost.
The price of the thing after applying 15% discount is $110.50.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The price at which thing is purchased = $130.
Since, The salesperson forgot to give a discount of 15%.
The discounted price = 130 x 15 %
= 130 x 15/100
= 1950/100
= $19.5
The price after discount = 130 - 19.5 = 110.5
The required price after discount is $110.5.
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What is the exact value of cos(-60°)?
V3
2
Ni-
을
V3
2
Applying the cosine ratio of trigonometry, the exact value of cos(-60°) which equals cos (π/3) is: C. 1/2.
What is the Cosine Ratio?In trigonometry, the vaue of the cosine ratio is the cosine of the reference angle which equals the ratio of the adjcent side over the hypotenuse.
To get the exact value of cos(-60°), convert 60 to radians.
π radian = 180
60° = (π/3) radians
Note: cos (-θ) = cos θ
Therefore, cos (-π/3) = cos (π/3)
cos (π/3) = 1/2
The exact value of cos(-60°) = 1/2 (option C).
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What is x?
ONLY WRITE A NUMBER FOR YOUR ANSWER
If you need to round, round to the nearest tenth (one decimal place).
Please help, thank you!
Answer:
15
Step-by-step explanation:
to get from 10 to 25 you time by 2½
so then times 6 by 2½ and the answer is 15
Jerod hopes to earn $1200 in interest in 1.8 years time from $12,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$\stackrel{12000~~ + ~~1200}{13200}\\ P=\textit{original amount deposited}\dotfill &\$12000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1.8 \end{cases}[/tex]
[tex]13200=12000\left(1+\frac{~\frac{r}{100}~}{1}\right)^{1\cdot 1.8}\implies \cfrac{13200}{12000}=\left( 1+\cfrac{r}{100} \right)^{1.8} \\\\\\ \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{1.8}\implies \cfrac{11}{10}=\left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \\\\\\ \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\left[ \left(\cfrac{100 + r}{100} \right)^{\frac{9}{5}} \right]^{\frac{5}{9}}\implies \left( \cfrac{11}{10} \right)^{\frac{5}{9}}=\cfrac{100+r}{100}[/tex]
[tex]\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=\cfrac{100+r}{100}\implies 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}=100+r \\\\\\ 100\sqrt[9]{\left( \cfrac{11}{10} \right)^5}-100 = r\implies 5.44\approx r[/tex]
What is the median of the data set 11,13,15,21,23,31,31,33?
A. 31
B. 21
OC. 23
D. 22
Median:
The median in this set is the 5th term.
Therefore the median in this set is 23.
Which is more, 1 pound or 22 ounces?
Answer:
22 ounces is more
Step-by-step explanation:
1 pound is equal to 16 ounces
Answer:
1 pound
Step-by-step explanation:
1pound=16oz 22oz= 1.375pound
Pythagorean Theorem
solve for the missing side . Round to the nearest 10th
I NEED HELP ASAP I WILL MARK BRAINLIEST IF ANSWERED CORRECTLY NO LINKS IF YOU DO NOT KNOW THE ANSWER DONT COMMENT ON THIS THREAD
Answer:
\sqrt{45}
Step-by-step explanation:
A^2+B^2=C^2
36+?=81
81-36=45
[tex]\sqrt{45}[/tex]=
Answer:
6.7 mmStep-by-step explanation:
Pythagorean Theorem
a² + b² = c²Here, we are missing one of the altitudes, so we can arrange the equation to form :
a² = c² - b²Solving
UW² = VW² - UV²UW² = (9)² - (6)²UW² = 81 - 36UW² = 45UW = √45UW = 6.7 mmFind the area of the shaded shape. Write the area in square units
Answer:
length times width equals area LxW=Area
Step-by-step explanation:
so,
4 times 4= 26 yards
1=4 square yards
then 26X4 = 104 square yards
Answer:
Step-by-step explanation:
What is the scale factor from ABC to DEF?
Answer:
3
Step-by-step explanation:
3 to get to 15, multiply by 3, same for other sides.
Answer:
C
Step-by-step explanation:
9 divided by 3 is 3, 15 divided by 5 is 3, and 12 divided by 4 is 3. it all adds up to three
please help me find the total area of the composite figure below (geometry)
Answer:
lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex] ⇒ Answer D is correct
Step-by-step explanation:
First, let us find the area of the semi-circle.
Area = [tex]\frac{1}{2}[/tex] × π × r²
Given that,
diameter of the semi-circle is ⇒ l
∴ radius ⇒ l / 2
Let us find it now.
Area = [tex]\frac{1}{2}[/tex] × π × r²
Area = [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]
Secondly, let us find the area of the rectangle.
Area = length × width
Given that,
length ⇒ l
width ⇒ w
Let us find it now.
Area = length × width
Area = l ×w
Area = lw
And now let us find the total area.
Total area = Area of the rectangle + Area of the semi - circle
Tota area = lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]
given: tangent TA is parallel to KM. Prove: KS = MS
When tangent TA is parallel to KM, it can be proved that KS = MS since they're congruent.
How to prove the tangent?It should be noted that when the tangent line TA is parallel to chord KM, it simply means that segment KS and MS are congruent.
Therefore, since they're congruent, SKM and SMK are equal. By the theorem of inscribed angle, we will have:
SKM = 1/2m(MS)
SKM = 1/2m(KS).
Since SKM = SMK
1/2m(MS) = 1/2m(KS).
MS = KS
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Pete and his sister, Sophie, play the game Space Mission Commander on their video game
console. Pete has already completed 27 missions. Sophie has only completed 13 missions.
From now on, Pete plans to complete 3 missions per week. Meanwhile, Sophie plans to
complete 5 missions per week.
At some point, Sophie will catch up to Pete. How many weeks will it take? How many
missions each will Pete and Sophie have completed?
Answer:
It will take 7 weeks for Sophie to catch up to Pete. Both of them will each have completed 48 missions.
Step-by-step explanation:
27 + 3x = 13 + 5x
27 + 3x - 3x = 13 + 5x - 3x
27 = 13 + 2x
27 - 13 = 13 + 2x - 13
14 = 2x
x = 7
27 + 3x
27 + 3(7)
27 + 21
48
13 + 5x
13 + 5(7)
13 + 35
48
Which prism has a greater volume?
really need help!! please help me.
Answer:
x=26
Step-by-step explanation:
Since they are complementary
2x+38⁰=90⁰
2x=90⁰-38⁰
2x=52⁰
x=26⁰
I hope it helped you
Answer:
x = 26.Step-by-step explanation:
This is self-explanatory, We just need to find the value of x by doing this:
2x° + 38° = 90°= 2x° = 90° - 38°= 90° - 38°= 52° ÷ 2°= 26°x° = 26°.Brainliest please. I didn't get one on this account.
A certain flight arrives on time 80
percent of the time. Suppose 131
flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 103
flights are on time.
(b) at least 103
flights are on time.
(c) fewer than 98
flights are on time.
(d) between 98
and 117
,
inclusive are on time.
Answer:
B at least 103 flights are on time. :)
Step-by-step explanation:
First we need to turn the percentage into a decimal :)
131 x 0.80 = 104.8
The answer should be B at least 103 flights are on time.
Have an amazing day!!
Please rate and mark brainliest!!
Solve the equation by factoring. 2x^2 = 28 – x
x = –3.5 or x = 4
x = 2 or x = –7
x = –2 or x = 7
x = –4 or x = 3.5
Answer:
The value of x = 3.5 or -4
Step-by-step explanation:
=> 2x² = 28 – x
=> 2x²+ x - 28 = 0
=> 2x² + 8x - 7x - 28 = 0
=> 2x ( x + 4 ) - 7 ( x + 4 ) = 0
=> (2x - 7 ) ( x + 4 )
=> x = 7/2 = 3.5 or x = -4
Answer:
x = –4 or x = 3.5
Step-by-step explanation:
[tex]2x^{2}=28-x\Longleftrightarrow 2x^{2}+x-28=0[/tex]
[tex]\Longleftrightarrow 2x^{2}-7x+8x-28=0[/tex]
[tex]\Longleftrightarrow x(2x-7)+4(2x-7)=0[/tex]
[tex]\Longleftrightarrow (2x-7)(x+4)=0 \ \ \ \ \text{factor out} \left( 2x-7\right)[/tex]
[tex]\Longleftrightarrow 2x-7=0 \ \ or\ x+4=0\ \ \ \ \text{(zero product rule)}[/tex]
[tex]\Longleftrightarrow x=\frac{7}{2} \ \ or\ x=-4[/tex]
The rectangles are similar Find X.
The solution is Option A.
The value of x is given from proportion and x = 10 1/2 or x = 10.5
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the first rectangle be A
The dimensions of the rectangle A = 4 by 3
Let the second rectangle be B
The dimensions of the rectangle B = 14 by x
The two rectangles A and B are similar , so
Now , the proportion equation will be
3 / 4 = x / 14
Multiply by 14 on both sides of the equation , we get
x = ( 14 × 3 ) / 4
x = 42/4
x = 10.5
The value of x = 10 1/2
Therefore , the value of x is 10 1/2
Hence , the value of x of the rectangle is 10 1/2
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what is 2/3 - 1/2 = in simplest form
Answer:
1/3
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
2/3-1/2 = find the denominator 3×2=6
4/6-3/6 = rewrite with a denominator of 6
(4-3)/6 = 1/6 subtract numerators
Learning Task 1: Read and solve the following problems. Use the 4-Step Plan by supplying the needed information in each letter below. 1. A resident lot has the shape of a parallelogram. Its base measures 20 meters. The distance between the 2 parallel sides is 8 meters. What is the area of the lot? 2. A triangular landscape has a base of 24 meters and a height of 12 meters. Find its area. 3. A trapezoidal lawn has an upper base of 16 meters and a lower base is 30 meters. The distance between the parallel bases is 10 meters. If the lawn is to be planted with Bermuda grass, how many square meters of Bermuda grass will be needed 4. A rectangular banner has a length of 5 meters and a width of 3 meters. Find the area. 5. What is the area of a soccer ground square in shape with a side of 8 meters? A = G= O= N= S = och sa A= och *You will use the letters in each problem above
The area of the lot with a shape of a parallelogram if its base measures 20 meters and the distance given is 160m².
How to calculate the area?Area of a parallelogram will be:
= Base × Height
= 20 × 8
= 160m²
The area of the triangular landscape that has a base of 24 meters and a height of 12 meters will be:
= 1/2 × base × height
= 1/2 × 24 × 12
= 144m²
The area of the trapezium will be:
= 1/2 × (a + b) × h
= 1/2 × (16 + 30) × 10
= 1/2 × 46 × 10
= 230m²
The area of the rectangular banner has a length of 5 meters and a width of 3 meters will be:
= Length × Width
= 5 × 3
= 15m²
The area of a soccer ground square in shape with a side of 8 meters will be:
= 8 × 8
= 64m²
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