Answer:
remainder: -400
Explanation:
[tex]\sf f(x) = 3x^5 + 4x^4 + 5[/tex]
divided by x + 3
x + 3 = 0x = -3insert x = -3 in the function
[tex]\sf f(x) = 3(-3)^5 + 4(-3)^4 + 5[/tex]
[tex]\sf f(-3) = -400[/tex]
Use the graph to answer the question.
On a coordinate plane, a circle has center (4, negative 1) and radius of 5.
Which equation describes the circle?
(x – 4)2 + (y + 1)2 = 25
(x – 4)2 + (y + 1)2 = 5
(x + 4)2 + (y – 1)2 = 25
(x + 4)2 + (y – 1)2 = 5
Answer: A
find the equation of a straight line which is parallel to the line with equation 5x+7y=14 and passes through a point (-2,-3)
Answer:
[tex]7y=-5x-11[/tex]
Step-by-step explanation:
Since it says the lines are parallel both of their gradients will be same.
so gradient of line 1 = [tex]y=\frac{14-5x}{7}[/tex] = [tex]y=\frac{14}{7}-\frac{5x}{7}[/tex]= [tex]-\frac{5}{7}[/tex]
so equation of line 2 = [tex]y-y_{1}=m(x-x_{1} )[/tex]
= [tex]y-(-3)_{}=\frac{-5}{7} (x-(-2)_{} )[/tex]
= [tex]y +3=-\frac{5}{7}x+\frac{10}{7}[/tex]
= [tex]y =-\frac{5x+10}{7}-3[/tex]
= [tex]7y=-5x-11[/tex]
Step-by-step explanation:
basically a line equation typically looks like
y = ax + b
with a being the slope, and b bent the y-intercept (y value when x = 0).
5x + 7y = 14
7y = -5x + 14
y = -5/7 x + 14/7 = -5/7 x + 2
so, wie know the slope of the original line : -5/7 .
any line parallel to it must have the same slope.
our desired line looks like
y = -5/7 x + b
to get b we use the provided point (-2, -3).
-3 = -5/7 × -2 + b = 10/7 + b
-21/7 = 10/7 + b
-31/7 = b
and the full equation is
y = -5/7 x - 31/7
7y = -5x - 31
5x + 7y = -31
A vacuum cleaner costs $68, and the full-replacement extended warranty costs $22. if the manufacturer sells 360,920 vacuum cleaners under warranty and must replace 15% of them to honor the warranties, how much will the replacement costs be? a. $4,258,856 b. $3,681,384 c. $1,191,036 d. $6,749,204
The cost of the 15 percent of replaced vacuum cleaner which are sold under warranty is $3,681,384. Option b is correct.
What is percentage ?Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
A vacuum cleaner costs $68, and the full-replacement extended warranty costs $22.
The manufacturer sells 360,920 vacuum cleaners under warranty and must replace 15% of them to honor the warranties. Thus, the number of vecuum cleaner replaced by manufacturer is,
[tex]n=\dfrac{15}{100}\times360,920\\n=54138[/tex]
The cost of one vacuum cleaner is $68. Thus the cost of 54138 vcacuum cleaner is,
[tex]C=54138\times68\\C=3681384[/tex]
Hence, the cost of the 15 percent of replaced vacuum cleaner which are sold under warranty is $3,681,384. Option b is correct.
Learn more about the percentage here;
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find the value of x to the nearest tenth
Answer:
27
Step-by-step explanation:
So in the triangle, we've got the angle as 64°. And, there's only an opposite value and the hypotenuse value therefore the trig function is sin.
According to SOHCAHTOA,
sin=opp/ hyp
sin 64°=x / 30
Cross- multiply, then
x= 30 × sin 64°
x= 26.963
x= 27.0(nearest tenth)
Please help with this problem.
Answer:
whats the problem it doesnt say anything
I’m don’t have much points please help
~Denki Kaminari here~
Answer:
JGH
Step-by-step explanation:
it can be proven because there is the measurement of "P".
hope this helps :D
What is the volume, in cubic in, of a cylinder with a height of 8 in and a base radius of
2 in, to the nearest tenths place?
Answer:
V=100.5
Step-by-step explanation:
hopes this helps
Picture blow………………….
ANSWER:
e. 4 and 2
f. 1 and 3
g. 5 and 6
h. 7 and 8
Ok done. Thank to me >:3
Multiply
−3/10xy (60xy^6)
[tex]-\frac{3}{10}xy (60xy^{6} )[/tex]
Answer:
[tex] - 18 {x}^{2} {y}^{7} [/tex]
Step-by-step explanation:
[tex] - \frac{3}{10} xy(60x {y}^{6} ) = - \frac{3}{10} (60) \times x \times x \times y \times {y}^{6} \\ = - 18 {x}^{2} {y}^{7} [/tex]
-
What is the vertex of f(x) = 5x^2 + 20x – 16?
Answer:
(-2, -36)
Step-by-step explanation:
This is written in Standard Form
[tex]f(x)=5x^{2} +20x-16[/tex]
[tex]ax^{2} +bx+c[/tex]
Convert to vertex form.
[tex]f(x)=a(x-h)^{2}+k[/tex]
[tex]f(x)=5(x+2)^{2}-36[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
A
Step-by-step explanation:
[tex]\frac{4}{5} + \frac{2}{5} = \frac{6}{5} \\Simple make it improper, resulting in answer A[/tex]
Hope this helps!
Please Help !!! The figure below is made of 2 rectangular prisms.
Answer:
124
Step-by-step explanation:
4*5*3
+
2*4*8
=124
Formula for volume of a rectangular prism is base x height.
HELPP A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
7
6
Red
Blue
Green
Yellow
Purple
12
19
19
Based on these results, express the probability that the next spin will land on blue as
a fraction in simplest form.
Answer: 2/21
Step-by-step explanation:
6/63= 2/21
how this is hard and im hating this right now :/
Answer:
[tex]\boxed{\dfrac{y}{x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\dfrac{1}{x} }{\dfrac{1}{y} } \ \text{can also be written as} \ \dfrac{1}{x} \div \dfrac{1}{y}[/tex]
-------------------------------------------
[tex]\rightarrow \dfrac{1}{x} \div \dfrac{1}{y}[/tex]
Simplifying the expression using "a ÷ b = a x 1/b"
[tex]\rightarrow \dfrac{1}{x} \times y[/tex]
[tex]\rightarrow \boxed{\dfrac{y}{x}}[/tex]
James is participating in a 8-mile walk to raise money for a charity. He has received $600 in fixed pledges
and raises $11 extra for every mile he walks. Use a point-slope equation to find the amount he will raise if
he completes the walk.
If he finishes the race, James will raise
Answer:688
Step-by-step explanation:600+(11x8)=x
x=total
600+88=x
x=688
x^2-8x+16=3 solve using square roots
Answer:
x = 4 ± [tex]\sqrt{3}[/tex]
Step-by-step explanation:
x² - 8x + 16 = 3 ← the left side is a perfect square
(x - 4)² = 3 ( take square root of both sides )
x - 4 = ± [tex]\sqrt{3}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{3}[/tex]
The first steps in writing f(x) = 3x2 – 24x 10 in vertex form are shown. f(x) = 3(x2 – 8x) 10 (startfraction negative 8 over 2 endfraction) squared = 16 what is the function written in vertex form? f(x) = 3(x 4)2 – 6 f(x) = 3(x 4)2 – 38 f(x) = 3(x – 4)2 – 6 f(x) = 3(x – 4)2 – 38
The given quadratic equation 3x^2 – 24x + 10 can be written in vertex form that is f(x) = 3(x – 4)2 – 38.
What are quadratic equations?A quadratic equation is an equation of degree 2 and the standard form of a quadratic equation [tex]ax^{2} +bx+c[/tex] where x is the variable and a,b, c are real numbers.
Following the steps already shown to transform the given function into the vertex form,
[tex]f(x) = 3(x^{2} - 8x + 16) + 10 - 3(16)\\f(x) = 3(x - 4)(x - 4) + 10 - 48\\f(x) = 3(x - 4)2 - 38[/tex]
Therefore, the function written in vertex form is f(x) = 3(x – 4)2 – 38.
Learn more about quadratic equations;
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Answer:
The answer is D!
Step-by-step explanation:
Solve for m
[tex]n=\frac{4}{5} (m+7)[/tex]
[tex]n=\dfrac 45 (m+7)\\\\\implies 5n = 4(m+7)\\\\\implies 5n = 4m+28\\\\\implies 4m = 5n-28\\\\\implies m = \dfrac{5n-28}{4}[/tex]
The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while
Robusta yields about 1200 kg per hectare. Suppose that a plantation has a
hectares of Arabica and r hectares of Robusta.
a. Write an equation relating a and r if the plantation yields 1,000,000 kg of coffee.
b. On August 14, 2003, the world market price of coffee was $1.42 per kg of Arabica
and $0.73 per kg of Robusta. Write an equation relating a and r if the plantation
produces coffee worth $1,000,000.
Answer:
See belowStep-by-step explanation:
a)
Arabica coffee = 750aRobusta coffee = 1200rThe total amount coffee beans
750a + 1200r = 1000000 kgb)
The total amount of market price
1.42*750a + 0.73*1200r = 1000000 ⇒1065a + 876r = 1000000 dollarsAnswer:
a) 750a + 1200r = 1000000
b) 1065a + 876r = 1000000
Step-by-step explanation:
Define the variables:
Let a = number of hectares of Arabica beansLet r = number of hectares of Robusta beansPart (a)
Given:
Arabica coffee = 750 kg beans per hectareRobusta coffee = 1200 kg beans per hectareIf the plantation yields 1,000,000 kg of coffee:
⇒ 750a + 1200r = 1000000
Part (b)
Given:
Arabica beans = $1.42 per kgRobusta beans = $0.73 per kgIf the price of Arabica beans is $1.42 per kg, and Arabica yields about 750 kg per hectare, then the price per hectare of Arabica coffee beans is:
⇒ $1.42 × 750 = $1065 per hectare
If the price of Robusta beans is $0.73 per kg, and Robusta yields about 1200 kg per hectare, then the price per hectare of Robusta coffee beans is:
⇒ $0.73 × 1200 = $876 per hectare
Therefore, if the plantation produces coffee worth $1,000,000:
⇒ 1065a + 876r = 1000000
You are standing at point C, 45 feet from the Point State Park fountain in Pittsburgh, PA. The distance from you to a point of tangency on the fountain is
105 feet. Find the length of AC, the distance between you and your friend at point A.
The tangent line DC is perpendicular to the radius of the park
The length of AC is 245 feet
How to determine the distance AC?To calculate the distance AC, we start by calculating the length of AB using:
DC^2 = (BC + AB) * BC
So, we have:
105^2 = (45 + AB) * 45
Evaluate the exponent
11025 = (45 + AB) * 45
Divide both sides by 45
245 = 45 + AB
Rewrite as:
AB + 45 = 245
From the figure, we have:
AC = AB + 45
Substitute AB + 45 = 245
AC = 245
Hence, the length of AC is 245 feet
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Please help me on this it’s due now
Answer:
I don't understand the question
on the same coordinate plane mark all points (x y) that satisfy the rule y=3x-2 SHOW GRAPH
The equation y = 3x - 2 is a linear equation
Points (0,2), (1,1) and (2,4) are on the line y = 3x - 2
How to determine the points?The rule is given as:
y = 3x - 2
Set x = 0
y = 3(0)- 2 = -2
Set x =1
y = 3(1)- 2 = 1
Set x = 2
y = 3(2)- 2 = 4
The above means that (0,2), (1,1) and (2,4) are on the line y = 3x - 2
See attachment for the graph of the line y = 3x - 2
Read more about linear equations at:
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Hello everyone i need help with the following question?
If x=3 and y=67
what is 6x × 8y + 27x - 6y + 3=
Answer:
9330
Step-by-step explanation:
6x × 8y + 27x - 6y + 3 = 18 × 536 + 81 - 402 + 3 =
9330
Answer:
The answer is 9330
Hope it helps
✧GHOSTOFSPARTA✧
What is the volume of this triangular prism?
Answer:
[tex]\text { The volume }=288 \mathrm{ft}^{3}[/tex]
Step-by-step explanation:
let V be the volume of the prism
B The area of the base which is a triangle
h is the height of the prism
______
Formula:
V = B × h
________
[tex]\begin{aligned}B &=\frac{9 \times 4}{2} \\&=\frac{36}{2} \\&=18\end{aligned}[/tex]
h = 16
Now we calculate:
[tex]\begin{aligned}V &=B \times h \\&=18 \times 16 \\&=288\end{aligned}[/tex]
Michael bought 4 pairs of socks.
He paid $7.16 after using a $2-off
coupon. Write an equation that can
be used to find the regular price, p,
of a pair of socks.
Answer:
4p - 2=7.16 is a formula that can be used to determine the standard price of a pair of socks.
Step-by-step explanation:
The information that we know is...
- Michael purchased four pairs of socks.
- After utilizing a $2 off coupon, he spent $7.16.
We're expected to figure out what formula we should apply to get the standard price of a pair of socks so...
We start by writing 4p.
4 represents a pair of socks, and p represents the normal price of socks.
4p - 2
Then subtract 2 since he utilized a $2 off coupon.
4p - 2 = 7.16
Lastly, add = 7.16 because he paid in total $7.16.
So, 4p - 2=7.16 is a formula that can be used to determine the standard price of a pair of socks.
Hope this helps! :D
How do you evaluate a geometric series?
To find the sum of a finite geometric series, use the formula, Sn=a1(1−rn)1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio .
hope it helps...!!!
Lindiwe is twice as old as Preeya and six years older than Sue . Their combined ages total 39 years . How old is Lindiwe
Answer:
Lindiwe is 18
Step-by-step explanation:
Lindiwe = L
Preeya = L/2
Sue = L-6
Their combined ages total 39 years
L+(L/2) + L-6 = 39
2.5L = 45
L=18
Lindiwe=18
Preeya= 9 (half of Lindiwe)
Sue = 12 (6 lessthan Lindiwe)
18+9+12 = 39
The yearly profits of a company is $52,000. The profits have been decreasing by 2.75% per year. What
will be the profits in 4 years?
A line passes through the point (-1,-5) and has a slope of -5.
Write an equation in slope-intercept form for this line.
We're given a point that the line intersects and its slope.
Let's use Point-slope:-
[tex]\boxed{y-y1=m(x-x1)}[/tex]
y1 = -5
m=-5
x1=-1
[tex]\boxed{y-(-5)=-5(x-(-1)}[/tex]
[tex]\boxed{y+5=-5(x+1)}[/tex]
Convert to slope-intercept:-
[tex]\boxed{y+5=-5x-5}[/tex]
[tex]\boxed{y=-5x-5-5}[/tex]
Finally,
[tex]\bigstar{\boxed{\pmb{y=-5x-10}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Express the first 10 terms of a sequence 2,5,8,11 in sigma notation