Answer:
[tex]\large \boxed{\sf \ \ \ a+b+c=3 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]4x^2+2x-1=4(x^2+\dfrac{2}{4}x)-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1[/tex]
As
[tex](x+\dfrac{1}{4})^2=x^2+\dfrac{2}{4}x+\dfrac{1^2}{4^2}=x^2+\dfrac{2}{4}x+\dfrac{1}{4^2} \ \ So \\\\x^2+\dfrac{2}{4}x=(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}[/tex]
Let 's go back to the first equation
[tex]4x^2+2x-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1=4(x+\dfrac{1}{4})^2-\dfrac{1}{4}-1\\\\=4(x+\dfrac{1}{4})^2-\dfrac{1+4}{4}=\boxed{4(x+\dfrac{1}{4})^2-\dfrac{5}{4}}[/tex]
a = 4
[tex]b=\dfrac{1}{4}\\\\c=-\dfrac{5}{4}[/tex]
[tex]a+b+c=4+\dfrac{1}{4}-\dfrac{5}{4}=\dfrac{4*4+1-5}{4}=\dfrac{12}{4}=3[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
9/13
Step-by-step explanation:
rise = y₂ - y₁ = -1 - (-10) = -1 + 10 = 9
run = x₂ - x₁ = 9 - (-4) = 9 + 4 = 13
Step-by-step explanation:
Rewrite the expression in exponential form.
Answer:
[tex]a^{\frac{1}{3} }[/tex]
Step-by-step explanation:
Apply rule: [tex]\displaystyle \sqrt[n]{x} =x^{\frac{1}{n}[/tex]
[tex]\sqrt[3]{a} =a^{\frac{1}{3} }[/tex]
please Evaluate 27 times ( 1/3) to the 3 power. A). 1 B). 3 C). 9 D). 27
Answer:
you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.
Step-by-step explanation:
27(1/3)^3
81^3
512
A traffic officer is compiling information about the relationship between the hour or the day and the speed over the limit at which the motorist is ticketed. He computes a correlation coefficient of 0.12. What does this tell the officer?
Answer:
The correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
The types of correlation coefficient are:
+1 (-1) : Perfect positive (negative) correlation0 to 0.30(-0.30) : Weak positive (negative) correlation0.30(-0.30) to 0.70(-0.70) : Moderate positive (negative) correlation0.70(-0.70) to 1 (-1) : Strong positive (negative) correlationThe correlation coefficient value between the hour of the day and the speed over the limit at which the motorist is ticketed is:
r = 0.12.
The value of r lies between:
0 < 0.12 < 0.30
Thus, the correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.
Which expression represents a factorization of 32m + 56mp?
A. 8(4m +7p)
B. 8(4 + 7)mp
C. 8p(4 + 7m)
D. 8m(4 + 7p)
Answer:
The answer is option D
Step-by-step explanation:
32m + 56mp
First factor out the HCF out
The HCF of 32and 56 is 8
So we have
8 ( 4m + 7mp)
next factor m out
We have the final answer as
8m( 4 + 7p)Hope this helps you
3x + 45 = 4x + 21
Solve for 'x'.
Answer:
Step-by-step explanation:
3x + 45 = 4x + 21
45 - 21 = 4x - 3x
24 = x
Answer:
x=24Step-by-step explanation:
[tex]3x + 45 = 4x + 21 \\ collect \: like \: terms \\ 3x - 4x = 21 - 45 \\ - x = - 24[/tex]
[tex]x = 24[/tex]
what is 23/20 as a mixed number
Answer:
[tex]1\frac{3}{20}[/tex]
Step-by-step explanation:
'23' fits into '20' one time. So, '1' would be the whole number. We would be left over with '[tex]\frac{3}{20}[/tex]' as the remainder, so '[tex]\frac{3}{20}[/tex]' would be the fraction of the mixed number.
Put them together, and you get: [tex]1\frac{3}{20}[/tex]
The fraction is already in it's simplest form.
Brainilest Appreciated.
The solution for mixed fraction of number 23 / 20 is,
⇒ 23/20 = 1 3/20
We have to given that,
A number is,
⇒ 23 / 20
We can divide it for the mixed fraction as,
⇒ 23 / 20
20 ) 23 ( 1
- 20
--------------
3
Therefore, It can be written as,
⇒ 23 / 20 = 1 3/20
Thus, The solution for mixed fraction of number 23 / 20 is,
⇒ 23/20 = 1 3/20
Learn more about the divide visit:
https://brainly.com/question/28119824
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The base radius of two circular cones of the same height are in the ratio 4:6.The ratio of their volume are ?
Answer:
64 : 216
Step-by-step explanation:
Given the ratio of the heights = a : b, then
ratio of volumes = a³ : b³
Here the ratio of heights = 4 : 6 = 2 : 3 ← in simplest form, thus
ratio of volumes = 4³ : 6³ = 64 : 216 = 8 : 27 ← in simplest form
carbon 14 is a radioactive element with a half life of 5750 years. A human skeleton is found to contain one fifth of its original amount of carbon 14. how old is the skeleton
Answer:
The skeleton is 1150 yrs old.
Step-by-step explanation:
To get this answer you would take 5750 and divide by 5 because the problem say 1/5th. This would give you the equation 5750/5 = 1150.
Two cars leave an intersection at the same time. One drives east while the other travels south at 15 miles per hour faster than the other. After 3 hours, the cars are 225 miles apart. How fast is the southbound car driving?
Answer:
60 mph
Step-by-step explanation:
Let 'S' be the velocity of the southbound car and 'E' be the velocity of the eastbound car. The distances traveled by each car are:
[tex]D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45[/tex]
The distance between both cars is given by:
[tex]D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\[/tex]
Solving the quadratic equation for the velocity of the eastbound car:
[tex]18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph[/tex]
The velocity of the southbound car is:
[tex]S=E+15=45+15\\S=60\ mph[/tex]
The southbound car is driving at 60 mph.
can anyone help me solve this function?
Answer:
5x +3
Step-by-step explanation:
f(x) = 2x-6
g(x) = 3x+9
(f+g) (x) = 2x-6+ 3x+9
Combine like terms
= 5x +3
We are given the following two equations:
[tex]f(x)=2x-6[/tex]
[tex]g(x)=3x+9[/tex]
To find (f+g)(x), we just add f(x) and g(x) and simplify:
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex]=2x-6+3x+9[/tex]
[tex]=5x+3[/tex]
Let me know if you need any clarifications, thanks!
given the side length of 35m and a height of 22m, calculate the length of the slant edge ( E ) the base angle the distance between the center of the base and the corner of the pyramid and the area of the side of the pyramid
Work shown please!
Answer:
1) 33.11 m
2) 58.1°
3) 35·√2
4) 491.925 m²
Step-by-step explanation:
Side length of the pyramid = 35 m
The height of the pyramid = 22 m
The slant height = √(Height² + (1/2 Side length)²)
The slant height = √(22² + (1/2×35)² = 28.11 m
1) The slant edge length = √((Slant height)² + (1/2 Side length)²
The slant edge length = √(28.11² + (1/2×35)²) = 33.11 m
2) The base angle = tan⁻¹((Slant height)/(1/2 Side length))
The base angle = tan⁻¹(28.11/(1/2×35)) = 58.1°
3) The distance between the center pf the base and the corner of the pyramid is half the length of the base diagonal
The length of the base diagonal = √((Side length)² + (Side length)²)
The length of the base diagonal = √(35² + 35²) = 35·√2
The distance between the center pf the base and the corner of the pyramid = 35·√2/2 = 24.75 cm
4) The area of the side of the pyramid = 1/2×(Side length)× (slant height)
The area of the side of the pyramid = 1/2*35*28.11 = 491.925 m²
Simplify: 3 · 32 + 8 ÷ 2 − (4 + 3)
Answer: 93
Step-by-step explanation:
To solve this we need to follow BIDMAS.
The order of calculations is brackets, division, then multiplication, then addition, then subtraction.
1) (4 + 3) = 7
2) Division: 8 / 2 = 4
3) Multiplication: 3 * 32 = 96
This leaves us with:
96 + 4 - 7
This equals 93.
Answer:
93
Step-by-step explanation:
3 · 32 + 8 ÷ 2 − (4 + 3)
PEMDAS says parentheses first
3 · 32 + 8 ÷ 2 − (7)
Then multiply and divide from left to right
96 + 4 -7
Then add and subtract
100-7
93
What the answer question
Answer:
[tex]\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}[/tex]
Step-by-step explanation:
m∠Z = 180° - 118° - 28° = 34°
[tex]\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\[/tex]
[tex]\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5[/tex]
What is the product of the polynomials below
Answer:
B. [tex]15x^{4}[/tex] + 2x³ - 8x² - 22x - 15
Step-by-step explanation:
1. (3x² - 2x - 3)(5x² + 4x +5)
[tex]15x^{4}[/tex] + 12x³ + 15x² - 10x³ - 8x² - 10x - 15x² - 12x - 15
2. Combine like terms
[tex]15x^{4}[/tex] + 2x³ - 8x² - 22x - 15
ANSWER QUICKLY plzzzzzz
Answer:
$95.42 more
Step-by-step explanation:
To find out how much money was made with Investment A after 2 years:
First, we are told that 160 dollars is saved per month for 2 years. There are 24 months in 2 years, so we have to multiply $160 by 24 months.
160 *24=$3840 after 2 years.
Next, we learn thar 2.5% interest rate is added to the total amount saved in those two years. So, we must turn 2.5% in to a decimal, which is 0.025.
Now, multiply 3840*0.025 to get $96.
We have to add that on the the amount saved, so 3840+96=$3936.
Investment A made $3936 after 2 years.
To find out how much money was made with Investment B.
So, we have to find compound interest. The formula for compound interest is:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
In this problem: P=3800, r=3% or 0.03, n=1, and t=2.
So, lets write it out: [tex]A=3800(1+\frac{0.03}{1} )^{2*1}[/tex]
That becomes: [tex]A=3800(1.03)^{2}[/tex]
Simplify it even further: [tex]A=3800(1.0609)[/tex]
Multiply the last two numbers to get: [tex]A=4031.42[/tex]
Investment B made $4031.42 after 2 years.
The question asks us to find out how much more money Investment B made than Investment A after 2 years. It's simple. Just subtract Investment A's amount from Investment B's amount.
4031.42-3936=95.42
Investment B made $95.42 more than Investment A after 2 years.
Solve for $x$, where $x > 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[tex]Solve for $x$, where $x \ \textgreater \ 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.[/tex]
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The solutions are, for a positive discriminant:
[tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]
Here, we have a = -21, b = -11, c = 40, so it gives:
[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]
So, we have two solutions:
[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]
We only want x > 0 so the solution is
[tex]\dfrac{8}{7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
h(x) = -15.6(x - 3.8)² + 241
Step-by-step explanation:
if you were to graph these equations, you can see that the second equation has a lower maximum than the rest of equations, including the original. therefore, that answer can be eliminated.
or simply recognize the equation is in vertex form and realize that 222 is the y-value of the vertex. and 222 < 230. (230 being the y-value of the parent function's vertex)
the a-value (-15.9 for the parent/original function) of the new equation must be less than the parent function's a-value. this is the rate at which the pumpkin is decreasing. the lower the value, the slower the pumpkin moves. this is an advantage, as the length it travels increases. therefore, the third and fourth options are eliminated, leaving the first option as the answer.
A circle with center A and radius three inches is tangent at C to a circle with center B, as shown. If point B is on the small circle, what is the area of the shaded region? Express your answer in terms of \pi.
Answer:
27π Sq in.
Step-by-step explanation:
Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.
If a equals 15, then what number does 2a - 5 equal?
Answer:
25
Step-by-step explanation:
a=15
2(15)-5=25
30-5=25
Answer:
25
Step-by-step explanation:
The problem substituting a for 15 would be 2(15)-5
2*15 is 30, then -5 is 25.
PLZ HELP ASAP!!! I WILL NAME BRAINLIEST!! 65 POINTS!! (:
Answer:
1. 44 + 3x
2. 2y - 8
3. x - 6
15. [tex]5\frac{7}{8}[/tex]
16. [tex]6\frac{1}{3}[/tex]
17. [tex]3\frac{7}{9}[/tex]
Step-by-step explanation:
1. 7² + 2² - 5 - 4 + 3x
49 + 4 - 5 - 4 + 3x
53 - 5 - 4 + 3x
48 - 4 + 3x
44 + 3x
2. - y - 5 + y + 2(2y-y) - 3
-y - 5 + y + 4y - 2y -3
-y - 5 + 5y - 2y - 3
4y - 2y - 5 - 3
2y - 8
3. 5x -3 - x - 3(x + 1²)
5x - 3 - x - 3x - 3
4x - 3x - 3 -3
x - 3 -3
x - 6
15. [tex]7\frac{1}{4} - 1\frac{3}{8}[/tex]
= [tex]7 \frac{2}{8} - 1\frac{3}{8}[/tex]
= [tex]\frac{58}{8} - \frac{11}{8}[/tex]
= [tex]\frac{47}{8}[/tex] → [tex]5\frac{7}{8}[/tex]
16. [tex]9 - 2\frac{2}{3}[/tex]
= [tex]\frac{54}{6} - 2\frac{4}{6}[/tex]
= [tex]\frac{54}{6} - \frac{16}{6}[/tex]
= [tex]\frac{38}{6}[/tex] → [tex]6\frac{2}{6}[/tex] → [tex]6\frac{1}{3}[/tex]
17. [tex]10\frac{1}{3} - 6\frac{5}{9}[/tex]
= [tex]10 \frac{3}{9} - 6\frac{5}{9}[/tex]
= [tex]\frac{93}{9} - \frac{59}{9}[/tex]
= [tex]\frac{34}{9}[/tex] → [tex]3\frac{7}{9}[/tex]
Hope this helps.
If the measure of ∠1 is 50°, what is the measure of ∠8?
Hey there! :)
Answer:
Measure of ∠8 is 130°.
Step-by-step explanation:
We can solve for ∠8 in multiple steps:
∠1 = 50°
∠5 = 50° due to corresponding angles being equivalent
180° - m∠5 = m∠8 due to supplementary angles
180° - 50° = m∠8 = 130°
Therefore, the measure of ∠8 is 130°.
Answer: The measure of angle 8 is 130 degrees.
Step-by-step explanation:
Angle 8 and angle 4 has the same measures. The same way angle 1 and angle 5 also have the same measures.So we know that angle 1 is 50 degrees so angle 5 is also 50 degrees. Angle 5 and 8 lies on a straight line.And straight lines have a measure of 180 degrees.So we know that angle 5 is 50 degrees so what angle measure will 50 degrees add up to get 180 degrees.
Use the equation
50 + x =180 solve for x
-50 -50
x = 130
This means angle 8 is 130 degrees .
which of the sequences is an arithmetic sequence
Answer:
it is C.
Step-by-step explanation:
The common difference is -7
-27 -(-20)= -27 + 20 = -7
-34 -(-27)= -34 + 27 = -7
-41 -(-34)= -41 + 34 = -7
-48 -(-41)= -48 + 41 = -7
AB =? Round your answer to the nearest hundredth.
Answer:
? = 4.41
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos A = adj / hyp
cos 25 = 4/?
? = 4/ cos 25
? =4.413511676
To the nearest hundredth
? = 4.41
Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
? = 57
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos ? = adj/ hyp
cos ? = 14/26
Taking the inverse cos of each side
cos ^-1 ( cos ?) = cos ^-1 ( 14/26)
? = 57.42102961
To the nearest degree
? = 57
Find all solutions of the equation in the interval [0, 2pi).
2 cos 0 - 13 = 0
Write your answer in radians in terms of t.
If there is more than one solution, separate them with commas.
Answer:
The solutions of 2·cos(θ) - √3 = 0in the interval [0, 2pi) are;
π/6, 13/6·π
Step-by-step explanation:
The given that the equation is 2·cos(θ) - √3 = 0
The solution of the above equation in the interval [0, 2pi) are required
Therefore, the domain includes 0 ≤ θ < 2pi
2·cos(θ) - √3 = 0
2·cos(θ) = √3
cos(θ) = √3/2
Therefore;
θ = cos⁻¹(√3/2)
The values are;
[tex]\theta =\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6} \, or \, \theta =-\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6}[/tex]
Where the domain is 0 ≤ θ < 2pi, we have;
π/6, 13/6·π
What are the solutions of the system? y=−6x−6 and y= x^2 −5x−6
Answer:
(0,-6) and (-1,0)
Step-by-step explanation:
First:
Set both sides equal to each other: -6x-6=x^2-5x-6
Next:
factor -6 our from the first side and write -5x as a difference:
-6(x+1)=x^2+x-6x-6
Then:
factor out x and -6 drom the second side:
-6(x+1)=x(x+1)-6(x-+1)
Then:
Factor out (x+1)
-6(x+1)=(x+1)(x-6)
Next Combine to one side and factor:
-(x+1)(6+x-6)=0
Simplify:
(x+1) (x)=0
find the zero:
x+1=0 --> x=-1
x=0 --> x=0
Substitute into the equations to find y:
y=-6(-1)-6
y=-6(0)-6
Solve:
y=0
y=-6
Answer:
(x1,y1)= (-1,0)
(x2,y2)= (0,-6)
Help please!!!!!!!!!!!!
Answer:
1/3
Step-by-step explanation:
Let's say you picked the blue one first. You have a 2/3 chance of doing that, and now you're left with 2. Now, to pick the green one, you have a 1/2 chance. Multiply that and you see that you have a 1/3 chance of picking it last.
Answer:
1/3.
Step-by-step explanation:
The probability that the red cube WON'T be picked on the first draw is 2/3. This is because there is a 1/3 probability of picking a green cube, added to a 1/3 probability of picking a blue cube.
The probability that the red cube WON'T be picked on the second draw is 1/2. This is because one cube has already been picked, so there are two remaining. You can only pick one of the two.
(2/3) * (1/2) = (2 * 1) / (3 * 2) = 2 / 6 = 1/3.
Hope this helps!
How many Real solutions
Answer:
A. 2 real roots: (2, 7) and (1, 4).
Step-by-step explanation:
y = x^2 + 3
y = 3x + 1
So equating the right sides:
x^2 + 3 = 3x + 1
x^2 - 3x + 2 = 0
(x - 2)(x - 1) = 0
So there are 2 roots.
They are x = 2 , y = 3(2) + 1 = 7 and
x = 1, y = 3(1) +1 = 4.
area perimeter for grade 4
Answer:
what is the questions.