Answer:
y = -4x + 2
Step-by-step explanation:
Given the following data;
Points (x1, y1) = (0, 2)
Perpendicular line = y = ¼x + 5
To find the equation of the straight line passing;
Mathematically, the equation of a straight line is given by the formula: y = mx + c
Where;
m is the slope.x and y are the pointsc is the intercept.From the question, we can deduce that the slope (m) of the perpendicular line is ¼.
y = ¼x + 5 = mx + c
Since the points are perpendicular to the equation of line, it must have a slope that is its negative reciprocal because the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, ¼ = -4
Next, we would write the equation of the straight line using the following formula;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - 2 = -4(x - 0)
y - 2 = -4x - 0
y - 2 = -4x
y = -4x + 2
For the triangle shown, what are the values of x and y?
60°
30°
6
Select the correct answer.
O x = 2V3, y = 473
O x= 3V3, y = 6/3
O x = 6/3, y = 12
O x = 6V3, y = 1273
Answer:
x = 6/√3 = 2√3
y = 2×2√3 = 4√3
So, 1st option is correct
Step by step solution please
Answer: A, C, D
Step-by-step explanation:
To find which logarith simplifies to 2, we first need to know how they work.
We now know that [tex]log_a(a^x)=x[/tex].
This tells us that only A, C, D would work.
[tex]8^2=64\\ \\6^2=36\\\\10^2=100[/tex]
Note: whenever you have a log that doesn;t specify the base, it is always 10, as shown in D.
Simplify
1/4(1 - 2/3)* + 1/3
Enter your answer in the box as a fraction in simplest form
Answer:
5/12
frsjnjjuvvffklomjyyrx
I am really confused on the graph anyone mind helping me
How do I solve this: h + 6/5 = 2
f(x) = Square root of quantity x plus seven. ; g(x) = 8x - 11 Find f(g(x)). (1 point)
f(g(x)) = 2 Square root of quantity two x plus one
f(g(x)) = 8 Square root of quantity x plus seven - 11
f(g(x)) = 8 Square root of quantity x plus four
f(g(x)) = 2 Square root of quantity two x minus one
Answer:
2 sqrt(2x-1)
Step-by-step explanation:
f(x) = sqrt(x+7)
g(x) = 8x-11
f(g(x))=
Place g(x) in for x in the function f(x)
f(g(x)) = sqrt( 8x-11 +7)
= sqrt( 8x -4)
Factor out 4
= sqrt( 4(2x-1)
= 2 sqrt(2x-1)
[tex]\\ \sf\longmapsto f(x)=\sqrt{x+7}[/tex]
[tex]\\ \sf\longmapsto g(x)=8x-11[/tex]
g(x) will be put on the place of x[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}[/tex]
.simplify
(2a+5)²-(a+3)(a-3)
Answer:
3a^2 + 20a + 34
Step-by-step explanation:
(2a + 5)^2 = 4a^2 + 20a + 25
(a +3)(a - 3) = a^2 - 9
Put these two partial answers together.
4a^2 + 20a + 25 -(a^2 -9 ) Remove the brackets.
4a^2 + 20a + 25 - a^2 + 9
4a^2 + 20a + 25 - a^2 + 9
3a^2 + 20a + 34
Answer: 3a² + 20a + 34
Concept:
When doing simplifying expressions, following the PEMDAS method would be easier.
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionWhen expanding parentheses, following the FOIL method would be easier.
FirstOuterInner LastSolve:
Given expression
(2a + 5)² - (a + 3) (a - 3)
Simplify exponenets
= (2a + 5) (2a + 5) - (a + 3) (a - 3)
Expand parentheses
= 4a² + 10a + 10a + 25 - (a² - 3a + 3a - 9)
= 4a² + 10a + 10a + 25 - a² + 3a - 3a + 9
Combine like terms
= 4a² - a² + 10a + 10a + 3a - 3a + 25 + 9
= 3a² + 20a + 34
Hope this helps!! :)
Please let me know if you have any questions
What is the average rate of change for this quadratic function for the interval
from x = 3 to X = 5?
Answer:
4
Step-by-step explanation:
average = mean of the data
(3 +5)/2
=8/2
=4
Answer:
8
Step-by-step explanation:
f(x2) -f(x1)
---------------
x2-x1
x2 = -3 and x1 = -5
Charlene is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of
items she sells. Suppose that x and y are related by the equation y=32x + 1900.
What is Charlene's total pay if she doesn't sell any items?
A. $32
B. $1,900
C. $3,200
D. $19
In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1
When the Center of dilation is inside the figure
The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilationWhen the Center of dilation is outside the figure
3. The original figure is closer to the the center of dilation
4. The dilated figure is closer to the center of dilation
The center of dilation is the fixed point from which the distances in a dilation are measured
The scale factor is ratio of the side lengths of an original figure or preimage to the side lengths of the newly formed image
Center of dilation is inside the figure
Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1, we have;The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation
Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure
2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;
The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation
Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure
Center of dilation outside the figure
3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;
The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure
4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1
The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation
Learn more about scale factors and center of dilation here;
https://brainly.com/question/12162455
what is the HCF of 7 and 13
Find the domain for the rational function f(x)=x+1/x-2
Step-by-step explanation:
here's the answer to your question
7.
Explain why the equation 6|x| + 25 = 15 has no solution.
When one solves, they arrive at a step where |x| is equal to a fraction that may not be represented as an integer. Since | x| must be an integer, there is no solution.
When one solves, they arrive at a step where x is equal to a negative number. Since x can never be negative inside of the absolute value bars, there is no solution.
When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution.
The statement is false. There is a solution.
Answer:
When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution.
Step-by-step explanation:
6|x| + 25 = 15
Subtract 25 from each side
6|x| + 25-25 = 15-25
6|x| = -10
Divide by 6
6|x| /6 = -10/6
|x| = -5/3
There is no solution because the absolute value must be greater than or equal to zero. This equation has it negative.
Find the square roots of these numbers by division method.
a-6090
What is the radius of a hemisphere with a volume of 885 in^3, to the nearest tenth of
an inch?
Answer:
The desired radius is r = 7.5 inches
Step-by-step explanation:
The formula for the volume of a sphere of radius r is V = (4/3)πr³. A hemisphere is half a full sphere, so the formula for the volume of a hemisphere of radius r is (4/3)(1/2)πr³, or (2/3)πr³.
We know that the volume of the hemisphere is 885 in³:
885 in³ = (2/3)πr³ and need to solve this first for r³ and then for r.
This is equivalent to:
885 in³ = (2π/3)r³.
We can now isolate r³ by multiplying both sides of this equation by (3 / [2π]):
(3 / [2π])(885 in³) = (3 / [2π])(2π/3)r³ = r³
Then r³ = 422.556 in³
Finally, we find the desired hemisphere radius by taking the cube root of both sides of the above equation:
r = ∛(422.556 in³) = 7.5 in (which is to the nearest tenth of an inch)
The desired radius is r = 7.5 inches
The value of -48 - x is positive. What are two possible values of x?
Show your work.
Please help I will give you Brainlyest
Answer:
-49
-50
Step-by-step explanation:
When a negative number subtracts another negative number, the number becomes positive.
For example: -48-(-49)=1
-48-(-49) becomes -48+49=1
In the rhombus, m angle 1 equals 106. What are m angles 2 and 3?
Answer:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320What does x equal? Dpsewbskdye
Answer:
x = 7
Step-by-step explanation:
27 = 7x + 6 - 4x (Given)
27 = 3x + 6 (Simplify)
27 - 6 = 3x + 6 - 6 (Subtract 6 on both sides)
21 = 3x (Simplify)
21/3 = 3x/3 (Divide 3 on both sides)
7 = x (Simplify)
6. Find an angle which is equal to its complement.
Answer:
x= 45
Step-by-step explanation:
Complementary angles equal 90 degrees
The angles are equal
x+x = 90
2x= 90
Divide by 2
2x/2 = 90/2
x= 45
Which functions have a maximum value greater than the maximum of the function g(x) = -(x + 3)2 - 4?
Answer:
max: -4
Step-by-step explanation:
(x+3)^2 》0 mọi x
<=> -(x+3)^2 《0
<=> -(x+3)^2 -4 《 -4
Determine whether the following polygons are similar.
Answer:
The polygons are NOT similar. The ratio of 12 to 18 equals 2 to 3, and the ratio of 26 to 32 equals 13 to 16. They're not the same, thus not similar.
Answer:
They are not similar, and the instructions says to put "None" otherwise, so...
Step-by-step explanation:
You can find this by dividing 32 by 16 to get something like 1.7777....
and dividing 26 by 12 should give the same ratio if they are similar, but it gives something like 2.1666...
Therefore they are not similar.
Congruent means two or more shapes are the same size and are similar, but for some things to be similar means that they have the same ratio, but not necessarily the same dimensions.
What is the product of three and the opposite is 4?
Product is multiplication.
The opposite of 4 is -4
3 x -4 = -12
Answer: -12
help me please brainliest for the best answer!!
Answer:
The volume of the irregular figure would be 102 [tex]cm^3[/tex].
Step-by-step explanation:
If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is [tex]l*w*h[/tex], where [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex], represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be [tex]6*3*5=30*3=90 cm^3[/tex], and the volume of the smaller rectangular prism would be [tex]3*2*2=6*2=12 cm^3[/tex]. So the volume of the entire irregular figure would be [tex]90+12=102 cm^3[/tex].
Answer:
102
Step-by-step explanation:
Large rectangle:
6 × 3 × 5 = 18 × 5 = 90
Small rectangle:
7 - 5 = 2
3 × 2 × 2 = 6 × 2 = 12
90 + 12 = 102
Hope this helped.
help! please!!!!!! look at photo :))
Hey there!
We know that Danielle earns $10 per hour, so muliply that by 3 and get 30.
Because Danielle works an extra half an hour, divide 10 by 2 and get 5.
Danielle earns $35 in 3 hours and a half.
Hope this helps! Please mark me as brainliest!
Have a wonderful day :)
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
Answer:
8/12 or 2/3
Where the first number is on the top and vice versa.
Step-by-step explanation:
gabys piggy bank contains nickles and dimes worth $5.15. If she has 66 coins in all, how many of each does she have
8.18
Step-by-step explanation:
8.18
pow pom wyh oqhw uwhwn 8.18 ge wk
Answer:
37 Dimes, 29 Nickels
Step-by-step explanation:
x= dimes
66-x = nickels
.1 (x) = dimes
.05 (66-x) = nickels
Solve
3.3 + 0.5x = 5.15
Solve again then you come out with
x= 37
66 - 37 = 29
Reflect Triangle ABC in BC. What kind of figure will result? How would your answer change if ABC is isosceles? a right triangle with right angle at A? a right isosceles trianglewith right angle at A?
9514 1404 393
Answer:
a kitea kite or rhombus, dependinga kitea squareStep-by-step explanation:
The reflections are illustrated in the attached.
A1, A1' are opposite vertices of the reflected original triangle. They are part of a kite figure.
A2, A2' are opposite vertices of a reflected isosceles triangle, where BA=BC. Figure A2BA2'C is a kite.
A2a, A2a' are opposite vertices of a reflected isosceles triangle with AB=AC. Figure A2aBA2a'C is a rhombus.
A3, A3' are opposite vertices of a right triangle with the right angle at A3. Figure A3BA3'C is a kite figure.
A4, A4' are opposite vertices of a reflected right isosceles triangle with AB=AC and the right angle at A4. Figure A4BA4'C is a square.
what is the intrest of rs2160 at the rate of 20% for 4years?in how many years will rs1800earn the same intrest at the rate of 12%
Answer:
considering it was simple interest,
We have the formula:
I = PRT ÷ 100
where,
I = InterestP = principalT = time (in years)R = ratefor the first part of the question,
P = Rs. 2160R = 20T = 4Thus, I = (2160 × 20 × 4)÷ 100
I = Rs. 1728
Now, for the second part,
P = Rs. 1800I = 1728R = 12T = 100×I÷PR
T = 100 × 1728÷(1800 × 12)
T = 8 Years
Please help explanation if possible
Answer:
y = | x-5|
Step-by-step explanation:
y = |x-h| +k where (h,k) is the center of the "v"
The "v" is located at (5,) so h=5 and k = 0
y = | x-5| +0
I'LL GIVE BRAINLIEST !!! FASTERR !
Answer:
Option A, 86°
Step-by-step explanation:
each diagonals of a rhombus divides the angles at half, so a+b+c+d = 360°/2 = 180°
now, a+b+c+d-94° = 180°-94° = 86°
Answer:
D 266°
Step-by-step explanation:
a+b+c+d-94°
90°+ 90°+ 90°+ 90° -94°
360°-94°
266°
