Answer:
[tex]y=4x+6[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope (also called the gradient) and b is the y-intercept (the value of y when x is 0)
1) Plug the gradient into the equation (b)
[tex]y=mx+b[/tex]
We're given that the gradient of the line is 4. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=4x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=4x+b[/tex]
Plug in the given point (1,10) as (x,y) and solve for b
[tex]10=4(1)+b\\10=4+b[/tex]
Subtract 4 from both sides to isolate b
[tex]10-4=4+b-4\\6=b[/tex]
Therefore, the y-intercept of the line is 6. Plug this back into [tex]y=4x+b[/tex] as b:
[tex]y=4x+6[/tex]
I hope this helps!
answer = y = 4x + 6
y = mx + b
gradient = slope = m = 4
(1,10) = (x,y)
plug in the values
10 = 4 (1) + b
10 = 4 + b
b = 6
y = 4x + 6
HELP ME ASAP I need help with this problem
B.
the solution is in the picture
Every 24 hours, Earth makes a full rotation around its axis. Earth's speed of rotation at the equator is 1.670 km per hour. What is the
circumference of Earth's equator?
(Hint. Earth's circumference at the equator is equal to the distance that Earth rotates around the equator).
Answer:
The circumference of Earth's equator is 40,080 km.
Step-by-step explanation:
Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:
24 x 1,670 = X
40,080 = X
Therefore, the circumference of Earth's equator is 40,080 km.
help asap please ------------------
Answer:
Correct answer 1
Step-by-step explanation:
Which is the equation of a line parallel to the line with the equation: y = 14x + 2
y = -4x - 7
y = 4x + 2
y = 14x − 12
y = −14x + 3
Hi!
y = ax + b
y = 14x + 2 → a = 14 ∧ b = 2
Parallel lines have the same slope factor (a) so line parallel to the line with the equation y = 14x + 2 will be y = 14x - 12
Write each as a percent. Use proportions.
7/25, 2/3, 3/8
Answer:
Step-by-step explanation:
[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]
(cos2a *cos 4a+ sin 2a*sin 4a)/sin4a
Answer:
Step-by-step explanation:
(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a
=[cos (4a-2a)]/sin 4a
=(cos 2a)/sin 4a
=(cos 2a) /(2 sin 2a cos 2a)
=1/(2 sin 2a)
=1/2 csc 2a
1 2 3 4 5 6 7 8 9 10 Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y, of the rectangular garden that she creates if one side is x feet long
Answer:
[tex]Area = 60x - x^2[/tex]
Step-by-step explanation:
Given
[tex]Perimeter = 120[/tex]
[tex]Side\ 1 = x[/tex]
Required
The area of the garden
First, we calculate the length of the other side using:
[tex]Perimeter = 2 *(Side\ 1 + Side\ 2)[/tex]
This gives:
[tex]120 = 2 *(x + Side\ 2)[/tex]
Divide both sides by 2
[tex]60 = x + Side\ 2[/tex]
Make Side 2 the subject
[tex]Side\ 2 = 60 - x[/tex]
So, the area of the garden is:
[tex]Area = Side\ 1 * Side\ 2[/tex]
[tex]Area = x * (60 - x)[/tex]
Expand
[tex]Area = 60x - x^2[/tex]
This afternoon Zoe left school, rode the bus 11/12 of a mile, and then walked 1/12 of a mile to get home. How much farther did Zoe ride than walk?
Write your answer as a fraction or as a whole or mixed number.
Answer:
Zoe rode [tex]\frac{5}{6}[/tex] of a mile more than she walked.
Step-by-step explanation:
[tex]\frac{11}{12}-\frac{1}{12} =\frac{5}{6}[/tex]
Using the slot method calculate the probability that you would roll 3 sixes
An amount of 25,000 is borrow for 15 years at 5.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer: [tex]55,811.91[/tex]
Step-by-step explanation:
Given
Principal amount is 25,000
Time Period is [tex]t=15\ yr[/tex]
Rate of interest [tex]r=5.5\%[/tex]
Amount in compound interest is given by
[tex]\Rightarrow A=P\left(1+r\%\right)^t[/tex]
Insert the values
[tex]\Rightarrow A=25,000(1+\dfrac{5.5}{100})^{15}\\\\\Rightarrow A=25,000(1.055)^{15}\\\Rightarrow A=55,811.91[/tex]
Therefore, [tex]55,811.91[/tex] must be paid back
Amanda is playing her new video game, Track Runner. At first, she earned 20 points for winning a sprint. Then in the next race, she got – 25 points when she knocked over most of her hurdles. What is Amanda's total score now? To solve the problem, Amy added 20+( – 25) and came up with an answer of 5 points. Is Amy correct? Why or why not?
Answer: Amy is incorrect. The answer is -5 points.
Step-by-step explanation:
From the question, we are informed that Amanda earned 20 points for winning a sprint in the first race but got -25 points in the second race.
Based on the information above, Amanda's total score now will be:
= 20 + (-25)
= 20 - 25
= -5
The answer is -5 points.
Amy is wrong because (+) × (-) = (-)
If the measure of angle 5 is (3x + 50) degrees and the measure of angle 6 is (5x + 16) degrees, what value of x will guarantee equation AB \\ DE
Answer:
x = 17
Step-by-step explanation:
If AB // DE, then angle 5 and angle 6 are alternate interior angle and they should be congruent.
5x + 16 = 3x + 50
Subtract 16 from both sides
5x = 3x + 50 - 16
5x = 3x + 34
Subtract 3x from both sides
5x - 3x = 34
2x = 34
Divide both sides by 2
x = 34/2
x = 17
Answer:
To AB \\ DEangle 5 should be equal to angle 63x + 50 = 5x + 16
5x - 3x = 50-16
2x = 34
x = 17
The function shown is a composition of the functions g(x) and h(x) .
f(x)=2x√+8−7
Which of the following shows a possible decomposition of the function f(x) ?
Find the measures of the angles formed by two intersecting lines if the
sum of the measures of three of the four angles is 270°
50 points! Please help quick!
Answer:
every single angle is 90°
Step-by-step explanation:
remember that,
4 angles will form if two lines intersect and the sum of those 4 angles is 360°
we are given the sum of 3 angles i.e 270
so one of the angles should be
[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]
simplify substraction:
[tex] \displaystyle {90}^{\circ}[/tex]
therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°
Answer:
90°
Step-by-step explanation:
We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°
Therefore :-
Measure of remaining one angle ,
360 - 270 90 °Therefore the measure of the fourth angle is 90°
What is the center of the circle:What is the center of the circle: (x+1)^2+(y-12)^2=25
1. 25
2. (1, -12)
3. 5
4. (-1, 12)
Answer:
option 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 1)² + (y - 12)² = 25 ← is in standard form
with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5
3. Can a regular polygon have an interior angle of 160°
the sum of interior angle is 180:
[tex]x + 160 = 180 \\ x = 180 - 160 \\ x = 20[/tex]
PLEASE HELP ASAP!
Cynthia bought a bag of wafers weighing 543 grams. There are about 0.035 ounces in 1 gram. About how many ounces does the
bag of wafers weigh?
OA.
15.51
B. 0.035
C. 0.64
OD
19.01
Answer:
19.005 ounces
Step-by-step explanation:
I believe that all you have to do is mutilply the 2 numbers which is 543 and 0.035 to find the amount of ounces it weighs. So 543 × 0.035 = 19.005. The answer is 19.005 ounces. (i hope)
You deposit $100 into a savings account that gives you 5.5% annual interest rate, compounded quarterly. What will be your balance after 4 years?
Answer:
$124.42.
Step-by-step explanation:
Given data
Principqp= $100
Rate= 5.5%
time=4 years
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt // Since we are compounding quarterly
A = 100.00(1 + 0.055/4)(^4)(4)
A = 100.00(1 + 0.01375)^(16)
A = $124.42
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 5.5% per year compounded 4 times per year over 4 years is $124.42.
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
find the percent of soccer and cross country kids in the fall
Sam rolls a fair dice and flips a fair coin.
What is the probability of obtaining an odd number and a head?
Answer:
The probability that this occurs is 25%, as 3/6 (chance to roll an odd number) multiplied by 1/2 (chance to flip a head) is .25.
Step-by-step explanation:
help pls!!
The functionſ is defined by f(x) = x(x + 3). If f(a) = 40 and a > 0, what is the value of a ?
A) 3
B) 5
C) 7
D) 8
Answer:
B) 5
Step-by-step explanation:
We are given the function:
[tex]f(x)=x(x+3)[/tex]
We are given that f(a) = 40 and a > 0 and we want to determine the value of a.
Substitute:
[tex]f(a)=40=a(a+3)[/tex]
Distribute:
[tex]a^2+3a=40[/tex]
Subtract 40 from both sides:
[tex]a^2+3a-40=0[/tex]
We can factor using 8 and -5. Hence:
[tex](a+8)(a-5)=0[/tex]
By the Zero Product Property:
[tex]a+8=0\text{ or } a-5=0[/tex]
Solve for each case:
[tex]\displaystyle a=-8\text{ or } a=5[/tex]
Since a > 0, we can eliminate the first solution. Hence:
[tex]a=5[/tex]
Our answer is B.
PLISSSSSS HELPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1.3
Step-by-step explanation:
The Rest Of Them Are Writen As Fractions
Answer:
[tex]\sqrt{10}[/tex]
NOTE: the other answer is WRONG...
irrational means can not be written as a fraction (with whole numbers)
4/3 = 1.33333333333
Step-by-step explanation:
At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?
Answer:
$765
Step-by-step explanation:
[tex]interest \: = \frac{prt}{100} \\ = \frac{(450)(5)(14)}{100} \\ = 315 \\ total \: money \: = 315 + 450 \\ = 765[/tex]
A(n) = 450 + (n – 1)(0.05 • 450); $765.00
Solve the equation and enter the value of x below. 4(x + 1) = 64
Answer:
15
Step-by-step explanation:
Use the distributive property
4x+4=64, then subtract
4x=60, then divide
x=15
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]4(x + 1) = 64 \\ 4x + 4 = 64 \\ 4x = 64 - 4 \\ 4x = 60 \\ x = \frac{60}{4} \\ x = 15[/tex]
=> The answer is 15.
I need help with 7 and 8 please
Answer:
Can't See 7 clearly
8) (9,9)
Step-by-step explanation:
[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]
Add x's and divide by 2
Add y's and divide by 2
Like taking the average of the coordinates.
Solve the following equa
8 (2v + 8) = 96
оа
v = 2
ii need help
Answer:
1
Step-by-step explanation:
64+32 =96 that'd how I got the answer
Answer:
[tex]{ \tt{8(2v + 8) = 96}} \\ { \tt{2v + 8 = 12}} \\ { \tt{2v = 4}} \\ { \bf{v = 2}}[/tex]
The following table shows a direct variation.
3 y
15 5
18 6
27 9
Answer:
Yes, it shows direct variation
Step-by-step explanation:
Given
The above table
Required
Is it a direct variation?
The constant of variation (k) is:
[tex]k = y/x[/tex]
For each pair x and y, we have:
[tex]k = 5/15 = 1/3[/tex]
[tex]k = 6/18 = 1/3[/tex]
[tex]k =9/27 = 1/3[/tex]
Since the calculate constant have the same value for all pair or x and y, then the table shows direct variation
Answer:1
Step-by-step explanation:3/3=1
Get three real world examples of a rectangle prism
Answer:
a shipping container ,the ones they use in large cargo ships
HELP WILL GIVE BRAINLIEST
Answer:
6
Step-by-step explanation:
Follow 1 hour on the y axis to where it meets the line of best fit. In this case it is about 6 puzzles.