The polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12. Then the correct option is D.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
According to the fundamental theorem of algebra.
The polynomial function has only exactly 6 roots.
The roots are the value of the variables in the polynomial at which the value of the polynomial is zero.
If the degree of the variable is n then the number of the roots will be n or less than n.
If the number of the roots are 6, then the degree of the variable will be 6 in the polynomial.
Then the polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12.
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Right triangles and trigonometry
Answer:
x = 13.83
Step-by-step explanation:
[tex]sin(70^{o}) =\frac{13}{x}[/tex]
[tex]x=\frac{13}{sin(70^{o} )} =13.83[/tex]
Hope this helps
scale drawing of a tree is 4% of the size of the actual tree. The height of the tree in
me drawing is 6 inches. What is the height of the actual tree, in feet?
how your work.
On the coordinate plane shown below, points H and F have coordinates ( − 2 , − 3 ) and ( − 4 , 2 ) , respectively. Use the distance formula to determine the straight line distance between points H and F . In your final answer, include all of your calculations.
Answer:
[tex]\sf \sqrt{29}[/tex]
Step-by-step explanation:
To find the distance between points H(-2, -3) and F(-4, 2), use the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Substitute the points into the distance formula and solve for d:
[tex]\begin{aligned}d&=\sqrt{(x_F-x_H)^2+(y_F-y_H)^2}\\\\&=\sqrt{(-4-(-2))^2+(2-(-3))^2}\\\\&=\sqrt{(-4+2)^2+(2+3)^2}\\\\&=\sqrt{(-2)^2+(5)^2}\\\\&=\sqrt{4+25}\\\\&=\sqrt{29}\end{aligned}[/tex]
Therefore, the exact distance between points H and F is [tex]\sf \sqrt{29}[/tex].
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Solve the following porportion.
x/25 = 2/5 x=
=========================================
Work Shown:
x/25 = 2/5
5x = 25*2
5x = 50
x = 50/5
x = 10
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Another approach:
x/25 = 2/5
x/25 = (2*5)/(5*5)
x/25 = 10/25
x = 10
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Yet another method:
x/25 = 2/5
x/25 = 0.4
x = 25*0.4
x = 10
Find the slope of the line 3x - y = 15
Answer:
3
Step-by-step explanation:
Rearrange in the slope-intercept form :
3x - y = 15y = 3x - 15Comparing this to the standard equation :
y = mx + cm = slopec = y-interceptOn comparing, it is clear that the slope of the line is 3If a figure has a line of symmetry, that means what?
The two sides of the shape are similar.
O The two sides are different shapes.
Both sides are exactly the same.
The two sides are different sizes.
Answer:
both sides are the same
Step-by-step explanation:
Find the surface area of a cylinder with a base radius of 5 cm and a height of 8 cm.
Use the value 3.14 for , and do not do any rounding.
Be sure to include the correct unit.
Answer:
408.40704
Step-by-step explanation:
Find the surface area of a cylinder with a height of 5 ft and a base radius of 4 ft.
Use the value 3.14 for x, and do not do any rounding.
Be sure to include the correct unit.
Answer:
A =281 ft^2
Step-by-step explanation:
A=2πrh+2πr^2
A = 2 (3.14) (4)(5) + 2 (3.14) (5)^2
A =281 ft^2
What is the reference angle for 292°?
O A. 12°
O B. 22°
O C. 68°
O D. 78°
C. 68°
292° lies on 4th quadrant.
Reference angle:1st quadrant: angle
2nd quadrant: 180° - angle
3rd quadrant: angle - 180°
4th quadrant: 360° - angle
So, reference angle: 360° - 292° = 68°
At best buy , they were having a great deal , for every $200 you spend , you get an anything 50% off coupon . If sarah spent $600 dollars on electronics , how many coupons would she get ?
Answer: 3 coupons
Step-by-step explanation:
We will divide the total amount of money spent by the amount of money needed to spend to receive a coupon.
$600 / $200 = 3
Sarah would get 3 coupons.
find the prime factorization of 405
Answer:
The factorisation of 405
405 = 5x3x3x3x3
Answer:
405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5
Step-by-step explanation:
I'll factor 405 with the Factor Tree Method.
Step 1: Place the number 405 on top of the factor tree.
Step 2: Notice that 405 can be divided by 5 -> 405 = 5 x 81. The two branches from 405 become 5 and 81.
Step 3: Continue factorizing other numbers in the tree until you are left only with the prime factors, which you cannot further factorize.
Step 4: Write the number as the product of prime factors you got.
405 = 3 x 3 x 3 x 3 x 5 = 3⁴ x 5
A children’s news and talk show is broadcasted for 2 hours each weekday. On Saturdays and Sundays, the show is an hour longer than during the week. How many hours is this show broadcasted each week?
A circle has radius 9.5 cm. Find the length of the arc intercepted by a central angle with measure 120°
Answer:
Step-by-step explanation:
Discussion
If the radius goes through 1 rotation. The "angle" gone through is 360 degrees. So the method is to figure out circumference of the circle, multiply this by a fraction involving 120, and you are done.
Formula
Arc Length = (120/360) * 2 * pi * r Substitute values into this equation.
Givens
Central angle = 120
r = 9.5
Solution
Arc Length = (120/360) * 2 * 3.14 * 9.5
Arc Length = (0.333) * 2 * 3.14 * 9.5
Arc Length = 19.87 cm
Help me please thank youuuuu ^_^
Answer:
x = 6
Step-by-step explanation:
2x - 3 = 9
so 9+3 = 12, and 12÷2 = 6
the value of x is 6
Pablo built a large wooden storage box. The box was in the shape of a rectangular prism, as shown below. He covered all the sides of the box with special wallpaper that cost a total of . How much did the wallpaper cost per square foot?
The cost of wallpaper used to cover all sides of the storage box is given by $3 per square foot
Cost of wallpaper per square footlength = 9 ftWidth = 8 ftHeight = 5 ftSurface area of a box = 2(lh + wh + lw)
= 2(9×5 + 8×5 + 9×8)
= 2(45 + 40 + 72)
= 2(157)
= 314 square foot
Total cost of wallpaper = $942Cost of wallpaper per square foot = $942 ÷ 314 square foot
= $3 per square foot
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Can someone please just check my answers over to make sure I got them right. Thank you so much!
Let me know if you need a close up on any of the pictures!
Answer: they are all correct congrats!
Step-by-step explanation:
Which of the following sets does not contain any irrational numbers?
PICTURE OF SETS SHOWN BELOW.
Thank you so much
Answer:
4 +311/59 answer IsD ong I know
which is greater, 2,670 meters or 2 kilometers? explain.
Answer: 2,670 meters
Step-by-step explanation:
2 kilometers = 2000 meters
2,670 > 2000
The greater value between 2,670 meters or 2 kilometers is 2,670 meters.
What is unit conversion?
It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We are given that;
Two measurements 2,670 meters or 2 kilometers
Now,
To compare 2,670 meters and 2 kilometers, we need to convert them to the same unit of measurement.
There are 1,000 meters in a kilometer. So 2 kilometers is equal to:
2 km * 1,000 m/km = 2,000 meters
Now we can compare 2,670 meters and 2,000 meters. We can see that 2,670 meters is greater than 2,000 meters, because 2,670 is a larger number than 2,000.
Therefore, by conversion the answer will be 2,670 meters is greater than 2 kilometers.
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solve by factoring x^2 + 8x =9
Answer:
[tex]x=-9,\:x=1[/tex]
Step-by-step explanation:
[tex]x^2+8x=9\\x^2+8x-9=0\\(x+9)(x-1)=0\\x=-9,\:x=1[/tex]
NO LINKS!!! Please help me with this graph. Part 6a
[tex]\large{\boxed{ \ g(x) = -\dfrac{7}{4} | x -5| +0 \ }}[/tex]
Explanation:Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (5, 0)
Take two points : (5, 0), (9, -7)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{-7-0}{9-5} \ = \ -\dfrac{7}{4}[/tex]
Join the variables together: [tex]\bf g(x) = - \dfrac{7}{4} | x -5| +0[/tex]
Answer:
[tex]f(x) = -\dfrac{7}{4}|x-5|+0 [/tex]
Step-by-step explanation:
The function in the coordinate Plane is an absolute value function . Consider the parent function
[tex]f(x) = |x| [/tex]
Recall the properties of transformation
f(x+a), If a<0 ⇒ It moves to righta.f(x),If a<0 ⇒ It flips upsidedownf(x)+a,If a>0 ⇒ It moves up & a<0 It moves downFrom the inspection of the graph,It has moved to right by 5 units, Thus
[tex]f(x - 5) = |x - 5| [/tex]
Apparently, It has neither shifted up or down, hence
[tex]f(x - 5) +0= |x - 5|+0 [/tex]
Looking at the graph, we can see that it has been reflected vertically. It tells us we have to multiply it by a negative constant
[tex] -a f(x - 5) +0= -a |x - 5| +0[/tex]
take (9,7) to figure out a.
set x to 9 and the LHS expression to 7[tex] -a | 9- 5| =7[/tex]
Solving the equation yields:
[tex] \boxed{a = - \frac{7}{4} }[/tex]
hence, our function is [tex]\boxed{f(x) = -\dfrac{7}{4}|x-5|+0} [/tex]
if the area of a triangle is 64 and the height is 10 what is the base
| 3. Two lines are intersecting. What is the
value of x?
(x+23)
(2x + 4)°
Answer:
Step-by-step explanation:
2x + 4 + x + 23 = 180
3x + 27 = 180
3x = 153
x = 51
I need help in this question
Answer:
I am not entirely sure but The maximum is 500 and b $0.50
In which of the following do you expect the correlation coefficient to be negative?
Please help!!
From the four graphs presented, it is expected the only one with a negative correlation coefficient is the third graph or graph c.
What is a negative correlation?This occurs when the two variables analyzed go in opposite direction, which means one increases and the other decreases.
How is this represented in a graph?In a graph, a negative correlation coefficient is related to a negative slope.
This negative slope can be seen in the third graph or graph C.
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How many terms are in this expression?
9x3+1+z
Evaluate the following indefinite integral
Step-by-step explanation:
try this solution, the answer is underlined with orange colour.
find g(-3) g(2) g(4)
g(-3) = 0.5 =
[tex] \frac{1}{2} [/tex]
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
g(2) as defined = 2
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
g(4)= 8-4 = 4
does anyone know the answer?
Answer: Choice A
40.61 square meters
==========================================================
Explanation:
The area of a full circle is
A = pi*r^2
meaning half of it (aka semicircle) will have this area
A = 0.5*pi*r^2
The diameter of the semicircle is 5.4 meters, which divides in half to get the radius of r = 2.7
The semicircle has an area of...
A = 0.5*pi*r^2
A = 0.5*3.14*(2.7)^2
A = 11.4453
which is approximate since pi = 3.14 is approximate.
Now compute the area of the triangle
area = base*height/2 = 5.4*10.8/2 = 29.16
Then add those sub-areas to get the grand total area.
semicircleArea + triangleArea = 11.4453+29.16 = 40.6053
That rounds to 40.61 which shows why choice A is the answer.
Solve 12x
x + 16 - 1 = 0
Answer:
xx=-0.8
Step-by-step explanation:
not sure if this is right because the 12xx is kind of strange
12xx+16-1=0
12xx+15=0
12xx=-15
12/12xx=12/-15
xx=-.8
A pizza shop has available toppings of bacon, sausage, pepperoni, onions, mushrooms, peppers and anchovies. How many different ways can a pizza be made with 3 toppings?
The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).
What is Combination?The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}
where,
n is the number of choices available,
r is the choices to be made.
The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).
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