The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are given by x = 4, x = 2 or x = -7
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that x + 7 is the root of 5x³ + 5x² - 170x + 280, hence:
(5x³ + 5x² - 170x + 280) / (x + 7) = 5x² - 30x - 40
Hence:
(5x³ + 5x² - 170x + 280) = (x + 7)(5x² - 30x - 40)
= 5(x² - 6x - 8)(x + 7)
= 5(x - 4)(x - 2)(x + 7)
The roots are at:
0 = 5(x - 4)(x - 2)(x + 7)
x = 4, x = 2 or x = -7
The roots of 5x³ + 5x² - 170x + 280 are x = 4, x = 2 or x = -7
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What does the constant of variation of 340 represent in this situation? total number of waves height of the waves in meters speed of the waves in meters per second time in seconds for one wave to pass a given point
Answer:
C: Speed of the waves in meters per second
Step-by-step explanation:
on edge
The frequency is inversely proportional to the time. Then the correct option is D.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.
The table is given below.
The constant variation of 340 represents this situation will be
The frequency is inversely proportional to the time. Then it represents time in seconds.
More about the wavelength link is given below.
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5. Mrs. Taylor painted her bathroom.
She began painting at 10:45 a.m.
She painted for 3 hours and 45
minutes. What time did she
finish painting?
A. 1:30 p.m.
B. 1:45 a.m.
C. 2:15 a.m.
D. 2:30 p.m.
Answer:
D
Step-by-step explanation:
Add 10:45 by 3
A racerunner is 26. 7 cm long. How much less than a meter is this?
Answer:
73.3 cm
Step-by-step explanation:
find the height and area of the equilateral triangle
As here we are given with an equilateral triangle, whose side is 3 cm, and we need to find the height and area of the equilateral triangle. So, for this let's recall that, the area of any equilateral triangle with side a is given by ;
[tex]{\boxed{\bf{Area_{(Equilateral\:\: Triangle)}=\dfrac{\sqrt{3}}{4}a^{2}}}}[/tex]So, if we substitute a = 3, in our Formula, it will yield to
[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(3)^{2}}[/tex]
[tex]{:\implies \quad \sf Area_{(Equilateral\:\:Triangle)}=\dfrac{\sqrt{3}}{4}(9)}[/tex]
[tex]{:\implies \quad \boxed{\bf{Area_{(Equilateral\:\:Triangle)}=\dfrac{9\sqrt{3}}{4}\:\:cm^{2}}}}[/tex]
Now, as we know that, for any triangle we also have a formula that is ;
[tex]{\boxed{\bf{Area_{(Triangle)}=\dfrac{1}{2}\times Base\times Height}}}[/tex]Now, Here as the triangle is equilateral, so it's base will just be same 3, and if we let height be H, so we will be having
[tex]{:\implies \quad \sf \dfrac{1}{2}\times 3\times H=\dfrac{9\sqrt{3}}{4}}[/tex]
[tex]{:\implies \quad \sf H=\dfrac{9\sqrt{3}}{4}\times \dfrac23}[/tex]
[tex]{:\implies \quad \boxed{\bf{Height=\dfrac{3\sqrt{3}}{2}\:\:cm}}}[/tex]
If a baseball card appreciates exponentially in value by 50% over 10 years, what is its annual appreciation (growth) rate? Please use a calculator, and answer to the nearest whole percent.
Using an exponential function, it is found that it's annual growth rate is of 4%.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the card appreciates exponentially in value by 50% over 10 years, hence:
A(10) = 1.5A(0).
Thus:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]1.5A(0) = A(0)(1 + r)^{10}[/tex]
[tex](1 + r)^{10} = 1.5[/tex]
[tex]\sqrt[10]{(1 + r)^{10}} = \sqrt[10]{1.5}[/tex]
1 + r = 1.04.
r = 0.04.
0.04 x 100% = 4%.
It's annual growth rate is of 4%.
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Help help with this question
Answer:
y-intercept: 4
slope: 2
Step-by-step explanation:
1/200
written as a finite decimal work shown
What is the value of x in the matrix equation below?
Answer:
-3
Step-by-step explanation:
Solving quadratic equations using the quadratic formula.
Answer:
what is there supposed to be a picture
Answer:
Down Here ↓↓↓
Step-by-step explanation:
Hello!
Standard Form of a Quadratic: [tex]ax^2 + bx +c[/tex]
Quadratic Formula: [tex]x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
To solve a quadratic using the quadratic formula, you have to plug values in for "a", "b", and "c" into the quadratic equation. Let's go over an example question.
Question: [tex]2x^2 +4x+2[/tex]
Solution:
Determine the values of "a", "b", and "c".
a = 2b = 4c = 2Plug it into the quadratic equation to solve.
Solve:
[tex]x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex][tex]x = \frac{-(4) \pm\sqrt{(4)^2-4(2)(2)}}{2(2)}[/tex][tex]x = \frac{-4 \pm\sqrt{16 - 16}}{4}[/tex][tex]x = \frac{-4 \pm\sqrt{0}}{4}[/tex][tex]x = \frac{-4}{4}[/tex][tex]x = -1[/tex]The value of x is -1.
Is (1,9) a solution to this system of equations?
y=5x+4
y=2x+7
Answer:
yes , if you substitute X (1) in both the equations you will get y=9 and if you substitute y(9) in both the equations you will get X=1
what is the rule for the numbers 1; 2; 4; 7; 11; 16
Answer:
n²+n+2
Step-by-step explanation:
1)Find the difference between the numbers.
Difference= +1,+2,+3,+4,+5
2)Find the second difference between the first differences.
Difference= +1 each time
2 differences=Quadratic sequence
3)Quadratic Sequence Equation= an²+bn+c
Find the values of a, b and c by using these terms:
a (bottom)
2a+b (middle)
a+b+c (top)
4)Substitute values into equation
a=1 b=1 c=2
n²+n+2
An auto dealer reduces the prices on the cars on the sales lot. The owner of the lot is planning on lowering the price of the cars by 4% each week. The original price was $22,000. B. Write the recursive routine.
Can someone help me, please and i will mark the person that get it right brainiest
Answer:
(a) Grade 6
Step-by-step explanation:
You want to know which grade (6 or 7) has the higher mean score, based on the given dot plots.
RangeThe scores of Grade 6 range from 70 to 100. Those of grade 7 range from 50 to 80.
MeanBoth distributions are approximately symmetrical, but have slightly more scores farther below the middle of the range than above. This means the mean in each case will be slightly below the middle of the range.
Even so, the mean of Grade 6 scores will be substantially above the mean of Grade 7 scores. Grade 6 has the higher mean score.
__
Additional comment
Assume the mean of Grade 6 is 85, the middle of the range of scores. Subtract the fewest number of dots (4) from each column, and we have 2 scores 15 units below that assumed mean, and 2 scores at 5 units above that assumed mean. The total of these is 2(-15) +2(+5) = -20. This tells us the actual mean of Grade 6 scores is -20/20 = -1 from the assumed mean of 85. The Grade 6 mean is 84. This is higher than any Grade 7 score, so Grade 6 must have the higher mean.
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Which is the graph of the solution set of 5 - 2 > 5?
O A.
-18
o
18
42
O B.
-18
0
18
42
+
Oc.
-18
O
+
18
42
D.
-18
+
0
18
42
Answer:
OC
Step-by-step explanation:
I got it right on my test!
Can someone please help me I need it asap!! I’ll give brainlist !!!
Answer:
[tex]6^{6}[/tex]
Step-by-step explanation:
When the coefficient is the same (in this case it is 6), you can subtract the exponents when it's being divided.
So in this case, the exponents are 9 and 3. The 9 is being divided by the 3, So:
[tex]6^{9-3}[/tex]
[tex]6^{6}[/tex]
Jordan wants to put wire fence around each of his tomato plants. He has a partial roll of fencing which is 18 1/6 feet long. How many tomato plants will Jordan be able to put a fence around using this roll if each plant requires exactly 2 2/3 feet of fencing.
Answer:
6 tomato plants
Step-by-step explanation:
[tex]18\frac{1}{6}= \frac{18\times6+1}{6}=\frac{108+1}{6}= \frac{109}{6}[/tex]
[tex]2\frac{2}{3}= \frac{2\times3+2}{3}=\frac{6+2}{3}= \frac{8}{3}[/tex]
then the number of tomato plants that Jordan will be able to put a fence around using this roll :
[tex]\frac{\frac{109}{6}}{\frac{8}{3}}= \frac{109}{6}}\times\frac{3}{8} = \frac{109}{2}}\times\frac{1}{8}= \frac{109}{16} = 6.8125[/tex]
then he can put fence only around 6 plants.
please help me with this thanks so much to whoever is helping me
Answer:
X = 80
Step-by-step explanation:
A flat line is equal to 180 degrees, meaning that if you use linear, you can find out that if you subtract 100 from it, it becomes 80, which resembles the X.
Tanisha, a manager at a state park, counted the money
in the cash register at the end of her shift, and then she
deposited the money in the bank. When she went back
to her office, she accidentally shredded the deposit
slip. She remembered that there were only $5 and $10
bills. She also recalled that there were 27 bills totaling
$205. How many $5 bills were in Tanisha's cash
register at the end of her shift?
Answer: 13
Step-by-step explanation:
[tex]$$Let $x$ be the number of \$5 bills \& let $y$ be the $10 \$$ bills.\\Then $x+y=27 \quad(\because$ total 27 bills $)$ - (1) \\ And $5 x+10 y=205 $\Rightarrow x+2 y=41 - (2)$$[/tex]
[tex]$$Now, (1) - (2) gives us.$$-y=14 \Rightarrow y=14$$Hence, $\quad x=13$\\So there were 13 \$5 bills.[/tex]
If your good at geometry please help me!
Jada's claim as a conjecture would be:
"All the segments in Δ ABC are parallel to the corresponding segments in Δ A'B'C' because both triangles are dilated from center P".
What is the implication of a dilation?
Whenever a shape is a dilation of another, we agree that the current shape and the dilated image's corresponding side lengths are in the same proportion and are all associated by the same scale factor, k.
What is the proof?
Attached are the images showing the parallelity of the segments and their corresponding lines.
Image 1 shows that Δ ABC and Δ A'B'C' are dilated from center p.Image 2 shows that Lines AB and A'B' run parallel to one another.Image 3 shows that lines CB and C'B' run parallel to one another.Image 4 shows that lines AC and A'C' run parallel to one another.
Hence, from the above, we can confirm that the above conjecture is true.
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What is the value of (-3 + 3) + (-2 + 3)?
O 5 - 61
0 -5 + 6
O 5 + 61
O 5-61
Answer:
Please check the question. As written, the value is 1, which is not amoung the answers
Step-by-step explanation:
(-3 + 3) + (-2 + 3)
(-3 + 3) = 0
(-2 + 3) = 1
0 + 1 = 1
Simplify:
((2x)/(3y ^ - 1)) ^ 2
Answer:
2xy²/9
Step-by-step explanation:
Jeans cost $38. They are on sale for 45% off. What is the sale price?
Show your work, please
Answer:
$20.9
Step-by-step explanation:
First you find what 45% of the cost is:
0.45 x 38 = 17.1
Then, because this is a special/decrease in original price, you subtract:
38 - 17.1 = 20.9
$20.9
How does knowing the coordinates of a point P in the Cartesian plane help you determine the trigonometric ratios associated with the angle formed between the initial and terminal arm for the angle? Use an example to help you explain.
The cosine and the sine of the angle are the x and y coordinates of P, respectively
The relationship between the coordinates and trigonometry ratiosAssume that the coordinate of a point P is:
P = (x,y)
The trigonometry ratios are represented using:
(cos(t), sin(t))= (x,y)
Where t represents the angle formed between the initial and terminal arm.
Hence, the cosine and the sine of the angle are the x and y coordinates of P, respectively
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Dana plans to use a survey of 60 randomly selected students at her school to predict the percentage of the 900 students at her school who will attend next week's school dance. How can Dana change her data collection plans to make her prediction closer to the actual result?
Answer:
See below ~
Step-by-step explanation:
Dana takes a survey of 60 students out of 900 total to see how many will attend the dance.
Based on whatever result she gets out of the 60 students, she can take that number and multiply it by 15 to get a closer prediction to the actual result.
This is because 60 x 15 = 900We are basic taking a ratio of the smaller portion so we can estimate the value of the larger groupA snack company can pack 12 granola bars in a box. How many boxes are needed for 600 granola bars?
A.5
B.720
C.50
D.7, 200
Answer:
The Answer is C. 50
Step-by-step explanation:
To pack 600 granola bars, 50 boxes are needed.
The correct option is C.
To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.
Number of boxes = Total granola bars / Granola bars per box
Number of boxes = 600 / 12
Number of boxes = 50
So, 50 boxes are needed to pack 600 granola bars.
The correct answer is option C: 50.
To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.
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Which rigid transformation(s) can map triangleabc onto trianglefed? reflection, then dilation reflection, then translation rotation, then translation rotation, then reflection
Answer:
rotation
Step-by-step explanation:
reflection
Answer:
rotation then translations-- C
Step-by-step explanation:
yes. and bc taking the quiz rn
m∠A=(y−16)° plese help me i really need this answer
I don't know what u r trying to find out so pls tell me what u r trying to find out.
But if u r trying to find out y here,
It is impossible to find out value of y, as we don't have the value of a or any other hints which will help in finding y.
But we can write the equation in a different way,
that is...
A - y = - 16°
1. The subject of the statement is also the _____ of the if-then form. *
1 point
Argument
Conclusion
Converse
Hypothesis
How many games did the team play? NO LINKS!!!
Answer:
blurry
Step-by-step explanation:
(8. 69×10to the power of 8)–(9. 6×10 to the power of 6
Answer:
3.25×10^15
Step-by-step explanation:
(8.69×10)^8_(9.6×10)^6. (3.25)×10^15_(7.83)×10^11=3.25×10^15