The factor are (x^2 - 6)(x + 5).
We have given the polynomial of [tex]x^3 + 5x^2 - 6x - 30.[/tex]
What is the grouping method?The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.
[tex]x^3 + 5x^2 - 6x - 30.[/tex]
factor out the x^2 from first two term and write the remaining term in the bracket
similarly,factor out 6 from the 3rd and 4th term we get
[tex]x^2(x+5)-6(x+5)[/tex]
by grouping are we get
[tex](x^2 - 6)(x + 5).[/tex]
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What is an equation that represents the linear
function described by the data in Item 5?
Please help:((
The equation that represents the linear function is y = 2x.
Linear equationA linear equation is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the y intercept.
Let us assume that from the table, we get the data with points (0, 0) and (2, 4). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{4-0}{2-0} (x-0)\\\\y=2x[/tex]
The equation that represents the linear function is y = 2x.
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Answer:
Step-by-step explanation:
answer is -10
find the value of the variables, giving brief reasons for your answer:
Answer:
a = 70°
b = 80°
Step-by-step explanation:
Angles on a straight line add up to 180°
⇒ a + 110 = 180
⇒ a = 180 - 110
⇒ a = 70°
The sum of the interior angles of a quadrilateral is 360°
⇒ a + b + 130 + 80 = 360
⇒ 70 + b + 130 + 80 = 360
⇒ b + 280 = 360
⇒ b = 360 - 280
⇒ b = 80°
HELLO CAN SOMEONE PLEASE ANSWER THIS QUESTION FOR ME I WILL MARK YOU THE BRAINLIEST AND I WILL GIVE YOU 5 STARS
Answer:
y=x-1
Step-by-step explanation:
Do the math. Just plug in x and y trust me it’s easy
Answer: y= x-1
Step-by-step explanation: y is always x minus 1 because -4 is one less than -3, 1 is one less than 2, and 4 is one less than 5.
Hey Inneeed helpppppppppp
Answer:
1 x 1/2 = 1/2
1/2 x 1/2 = 1/4
1/2 x 1/2 = 1/4
Step-by-step explanation:
Angel bought a piece of artwork that had a value of V dollars.
Over a period of five years the artwork increased in value by 40%.
Which expression represents the current value of the artwork?
A 1.4V
B 0.4v
C v+1.6v
D 1+0.4v
Using proportions, it is found that the expression that represents the current value of the artwork is given by:
A 1.4V
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the initial value was of V, which increased by 40%. Thus, the current value of V is 100% + 40% = 140% of the original, which is equivalent to a proportion of 1.4, that is: 1.4V.
Hence, option A represents the current value of the artwork.
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three cats and four dogs cost $145. at the same store, four cats and three dogs cost $135. Assuming each cat is the same price and each dog is the same price, what is the price, what is the price of 1 cat? what is the price of one dog?
Answer:
cat's price = $15
dog's price = $25
The brackets for a shelf are in the shape of a triangle ABC. Find the missing angle of the triangle if the measure of the angles a=33 and b=102
Answer:
45°Step-by-step explanation:
Sum of interior angles of a triangle is 180°.
Find the missing angle:
m∠A + m∠B + m∠C = 180°33° + 102° + m∠C = 180135° + m∠C = 180°m∠C = 180° - 135°m∠C = 45°[tex]\small\bold\green{[Sum \: of \: interior \: angles \: of \: a \: triangle \: is \: 180°]}[/tex]
Lets , Find the missing angle :
↪ m∠A + m∠B + m∠C = 180°
↪ 33° +102° + m² = 180°
↪ 135° + m∠C = 180°
↪ m∠C = 180° - 135°
↪ m∠C = 45°
pls help asap i need an anwser
Answer:
7.21 units
Step-by-step explanation:
Given points are: (-6, 6) and (-10, 0)
[tex]distance = \sqrt{ {( - 6 + 10)}^{2} + {(6 - 0)}^{2} } \\ \\ = \sqrt{ {(4)}^{2} + {(6)}^{2} } \\ \\ = \sqrt{ 16 + 36 } \\ \\ = \sqrt{ 52 } \\ \\ = 7.21 \: units[/tex]
-2/5 divided by -2/3?
Answer:
-3/5
Step-by-step explanation:
I used the KCF, or keep, change, flip, method for this.
The original problem is -2/5 divided by -2/3
We keep the first fraction - -2/5
change the sign to multiplication
and flip the second fraction - 3/2
so, -2/5 x 3/2
and then check for where we can simplify, we can in this instance:
-1/5 x 3/1
and then multiply across
-3/5
expand the expression below to find the values of capatilised pronumerals
PLS HELP :))
»(4x - 2y)(3x + 5y)
»4x(3x + 5y) + (-2y)(3x + 5y)
»12x² + 15xy - 6xy - 10y²
»12x² + 9xy - 10y²
so, ABC is :
A = 12✅B = 9✅C = -10✅complete the calculation so that each shows the correct sum 1.036 +blank =4
Answer:
-2.964
Step-by-step explanation:
i need help please thanks
Answer:
pick all 3 of the bottom row
Y'all know the drill (classify each triangle. Write acute, right, or obtuse) look at pic
Answer:
It is Right angle triangle.
Also it shows 90 degree angle at E.
I think it will help you.
How many weeks are in 1200 hours?
Enter your answer as a mixed number in simplest form in the box.
Please hurry! TEN COINS!!!
Answer:
7 1/7
Step-by-step explanation:
24 hours = 1 day
7 days = 1 week
⇒ number of hours in 1 week = 24 x 7 = 168
⇒ number of weeks in 1200 hrs = 1200 ÷ 168 = 7 1/7
If 2tanB+cotB=tanA,then proved that 2tan(A-B)=cotB
Answer:
it is so hard it's optional math bro I tried much
Step-by-step explanation:
hope others can give answers
Which expression is equivalent to (xy^5)^2(3x^4y)^3?
Need help on this I don't get it
Step-by-step explanation:
It is not a solution because the point falls outside the shaded region, if you were to plugin the point it would return a false statement
I need some help with this monomial....
15a^16b^11/(3a^4b^2)^3
Answer:
[tex]\frac{5a^4b^5}{9}[/tex]
Step-by-step explanation:
[tex]\frac{15a^1^6b^1^1}{(3a^4b^2)^3}[/tex]
[tex]=\frac{15a^1^6b^1^1}{27a^1^2b^6}[/tex]
[tex]=\frac{15a^4b^5}{27}[/tex]
[tex]=\frac{5a^4b^5}{9}[/tex]
Answer = [tex]=\frac{5a^4b^5}{9}[/tex]
Swedish researchers investigated the relationship between chocolate consumption and stroke. the researchers gave a questionnaire about eating habits to a randomly selected sample of swedish men. based on the responses to the questionnaire, the men were classified into two groups. group a consisted of the 9,250 men who ate the most chocolate per week, and group b consisted of the 9,250 men who ate the least chocolate per week. the researchers tracked the men's health for ten years. during that time, there were 458 cases of stroke among the men in group a and 543 cases of stroke among the men in group
A. Do the data provide convincing statistical evidence that Swedish men who would be classified into group A have a lower probability of stroke than Swedish men who would be classified into group B?
B. A report in a newspaper concluded that Swedish men can reduce their probability of stroke by eating more chocolate. Based on the description of the investigation was the conclusion appropriate? Justify your answer
Using the z-distribution, as we are working with a proportion, it is found that:
A. Yes, the data provides convincing statistical evidence that Swedish men who would be classified into group A have a lower probability of stroke than Swedish men who would be classified into group B.
B. Considering that the data provides statistical evidence, the conclusion was appropriate.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportions are the same, that is:
[tex]H_0: p_A - p_B = 0[/tex]
At the alternative hypothesis, it is tested proportion A is less than proportion B, that is:
[tex]H_1: p_A - p_B < 0[/tex]
What is the mean and the standard error for the distribution of difference of proportions?For each sample, they are given by:
[tex]p_A = \frac{458}{9250} = 0.0495, s_A = \sqrt{\frac{0.0495(0.9505)}{9250}} = 0.0023[/tex]
[tex]p_B = \frac{543}{9250} = 0.0587, s_B = \sqrt{\frac{0.0587(0.9413)}{9250}} = 0.0024[/tex]
Hence, for the distribution of differences, we have that:
[tex]\overline{p} = p_A - p_B = 0.0495 - 0.0587 = -0.0092[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0023^2 + 0.0024^2} = 0.0033[/tex]
What is the test statistic?It is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which p = 0 is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{-0.0092 - 0}{0.0033}[/tex]
[tex]z = -2.77[/tex]
Item a:
Considering a left-tailed test, as we are testing if the proportion is less than a value, with the standard significance level of 0.05, the critical value is of [tex]z^{\ast} = -1.645[/tex].
Since the test statistic is less than the critical value, it is found that yes, the data provides convincing statistical evidence that Swedish men who would be classified into group A have a lower probability of stroke than Swedish men who would be classified into group B.
Item b:
Considering that the data provides statistical evidence, the conclusion was appropriate.
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Olivia is making scarves. Each scarf will have 3 rectangles, and
2/3
of the rectangles will be purple.
How many purple rectangles does she need for 2 scarves?
Olivia needs
purple rectangles.
938 divided by 7, pls give the solution too
Answer:
134
Step-by-step explanation:
938÷7=134
Please help meeeee!!
Answer:
A parallelogram is a four sided shape, so this means that the total sum of interior angles is equal to 360 degrees.
It also has two sets of matching angles, therfore if it says one is 155 degrees it must have one more that is also 155 degrees.
This means 2 x 155= 310, 360 - 310 = 50 degrees remaining. This 50 degrees would be shared between the remaining two angles as they must be a matching pair also. 50 / 2=25.
This parallelogram has two angles of 155 and two of 25. Degrees.
Given a = 7.6, A = 50 degrees, and b = 4.3, use the Law of Sines to solve for B. Round
your answer to the nearest degree, and enter the number only. Note: The figure is
not drawn to scale.
Answer:
we need the figure, where is it
To decrease your household water usage by 10% a month means that a household using 4000 gallons of water a month would cut down to using
A blank gallons a month.
What is the quotient (2x2 + 10x + 12) ÷ (x + 3)?
Answer:
2x+4 or 2(x+2)
Step-by-step explanation:
I'm not very confident that I can give you a clear explanation while typing, but you can factor the equation which is one way how to do this.
2x^2 + 10x+12 = 2(x^2+5x+6)
= 2(x(x+3) + 2(x+3))
= 2(x+3)(x+2)
With that answer, you divide it by x+3 and get 2(x+2) or 2x+4
f(x)=-5x+1x=−5x+1, find f(6)
Answer:
f(x)=-5x+1x=−5x+1, find f(6)
f(6)= -5(6)+1(6)=-5(6)+1
F(6)=-24,-29
Each day the polar bear at Monroe's zoo eats 1/4 of a bucket of trout and 3/8 of a bucket of salmon how many buckets of fish does the polar bear eat daily
Answer:
5/8
Step-by-step explanation:
1/4=2/8
2/8+3/8=5/8
The speed of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,400 feet ahead of the first train is traveling at a constant speed of 96 feet per second and can be modeled by the function y = 96t + 1400. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
Taking into account the definition of a system of linear equations, the solution t=14 represents a viable time that the trains are side by side.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Calculation of time in this caseThe system of equations to be solved is
[tex]\left \{ {{y=14t^{2} } \atop {y=96t+1400}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the first equation in the second you get:
14t²= 96t +1400
Solving:
14t²- 96t -1400= 0
Being this a quadratic function of the form ax² + by +c, then it can be solved by: [tex]x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
In this case, being a=14, b=-96 and c=-1400, the equation is solved by:
[tex]t1=\frac{-(-96)+\sqrt{(-96)^{2} -4x14x(-1400)} }{2x14}[/tex]
[tex]t1=\frac{96+\sqrt{9216 +78400} }{28}[/tex]
[tex]t1=\frac{96+\sqrt{87616} }{28}[/tex]
[tex]t1=\frac{96+296}{28}[/tex]
[tex]t1=\frac{392}{28}[/tex]
t1=14
and
[tex]t2=\frac{-(-96)-\sqrt{(-96)^{2} -4x14x(-1400)} }{2x14}[/tex]
[tex]t2=\frac{96-\sqrt{9216 +78400} }{28}[/tex]
[tex]t2=\frac{96-\sqrt{87616} }{28}[/tex]
[tex]t2=\frac{96-296}{28}[/tex]
[tex]t2=\frac{-200}{28}[/tex]
t2= -7.14
Since time cannot be a negative value, the solution t=14 represents a viable time that the trains are side by side.
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Find the measures of the numbered angles in the kite shown to the right
Answer:
the sum of all angles in triangle is equal to 180°
Step-by-step explanation:
1 = 2 = 3 = 4 = 90° (360° / 4)
9 = 180° - 21° - 90° = 69°
10 = 180° - 59° - 90° = 31°
5 = 59°
6 = 21°
7 = 9 = 69°
8 = 10 = 31°
Find the value of x.
PLEASE HELP ME!!!!!!
Answer:
34 degrees
Step-by-step explanation:
sin(x) = opp/hyp = 9/16
So, x = 34.22 degrees
After rounding to the nearest degree, x = 34 degrees
