Answer:
13.8Step-by-step explanation:
if Points X and Z are on a number line and point Y partition line XZ into two parts where XY: YZ = 1:4, this can be expressed as;
XY/YZ = 1/4
cross multiply;
YZ = 4XY
Also, if The coordinate of X is 1.3, and the coordinate of Y is 3.8, then the distance XY will be expressed as XY = 3.8 - 1.3
XY = 2.5
YZ = 4(2.5)
YZ = 10
Since Y is at 3.8 and YZ is 10, then coordinate Z will be YZ + Y
coordinate of Z = 10+3.8
coordinate of Z = 13.8
Write g(x) = 40x 4x2 in vertex form. Write the function in standard form. Factor a out of the first two terms. Form a perfect square trinomial. Write the trinomial as a binomial squared. G(x) = 4x2 40x g(x) = 4(x2 10x) (ten-halves) squared = 25 g(x) = 4(x2 10x 25) – 4(25) g(x) = (x )2 –.
The vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).
What is the Equation of a parabola?The general equation of a parabola is given as,
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
As we want to write a function g(x) = 40x + 4x² in vertex form, and we know that the vertex form of a parabola, with vertex at (h,k) is written as,
[tex]f(x) = a(x-h)^2 + k[/tex]
Also, the algebraic identity [tex](x + a)^2[/tex] is written as,
[tex](x + a)^2 = x^2 + 2ax + a^2[/tex],
Therefore, [tex]x^2 + 2ax[/tex] can be written as
[tex]x^2 + 2ax = (x + a)^2 - a^2[/tex]
Further, we try to write the g(x) in the vertex form it can be written as,
[tex]\begin{aligned}g(x) &= 4x^2 + 40x\\\\ &= 4[x^2 + 10x]\\\\ &= 4[(x + 5)^2 - 5^2]\\\\ &= 4(x + 5)^2 - 100\\\end{aligned}[/tex]
Hence, the vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).
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Write and evaluate the expression. Then, select the correct answer. The sum of forty-five and a number; evaluate when n = 1. 1 45n; when n = 1. 1, the value is 49. 5. 45 n; when n = 1. 1, the value is 46. 1. 45 – n ; when n = 1. 1, the value is 43. 9. StartFraction n Over 45 EndFraction; when n = 1. 1, the value is 0. 24.
The sum of forty-five and a number n is 46.1, and the expression that can represent this can be written "45+n" where the value of n is 1.1
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The statement that is given to us is" the sum of forty-five and a number", therefore, the expression that will represent this can be written as,
45 + n,
Now, if the value of n is 1.1. Then the sum will be,
[tex]45+n\\\\=45+1.1\\\\=46.1[/tex]
Hence, the sum of forty-five and a number n is 46.1, and the expression that can represent this can be written "45+n" where the value of n is 1.1
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Select the correct answer.
Which of the equations below represents a line perpendicular to the x-axis?
ОА.
I = 3
ОВ.
= 3y
OC.
=y
OD.
I = -3y
Reset
Next
Answer
The anwser is B
Step-by-step explanation:
I did this test as well earlier this year
Equation x=3 represents a line perpendicular to the x-axis. Therefore, the correct answer is option A.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
here, we have,
A) x=3
Graph the line using the slope and y-intercept, or two points.
Slope: Undefined
y-intercept: No y-intercept
The coordinate points are (3, 0) and (3, 1).
B) Graph the line using the slope and y-intercept, or two points.
Slope: 1
y-intercept: (0,0)
The coordinate points are (0, 0) and (1, 1)
C) x=y
Graph the line using the slope and y-intercept, or two points.
Slope: 1
y-intercept: (0,0)
The coordinate points are (0, 0) and (1, 1)
D) x=-3y
Graph the line using the slope and y-intercept, or two points.
Slope: -1/3
y-intercept: (0,0)
The coordinate points are (0, 0) and (-3, 1)
Therefore, option A is the correct answer.
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Video
Mackenzie was offered a job that paid a
salary of $45,000 in its first year. The
salary was set to increase by 5% per year
every year. If Mackenzie worked at the job
for 17 years, what was the total amount of
money earned over the 17 years, to the
nearest whole number?
Answer:
103,140.82, or 103,141 since it asks for the whole number.
Step-by-step explanation:
[tex]45000(1.05)^17[/tex]
the 17 is supposed to be the whole power, not sure why the 7 is lower. but since she is making 45k a year, at a 5% increase in wages per year, this is how we would set up the equation. the number, multiplied by the percentage which is written as 1.05, since it is an increase, not a decrease, then we set that to the power of 17 since it is 17 years.
hope this helps, please mark as brainlest.
How do i write 2x+3y=24 as slope-intercept form?
Answer:
y = - [tex]\frac{2}{3}[/tex] x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y = 24 ( subtract 2x from both sides )
3y = - 2x + 24 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 8 ← in slope- intercept form
The equation 2x+3y=24 in the slope-intercept form can be written as [tex]y = -\frac{2}{3}x+8[/tex]
From the question,
We are to write the given equation in the slope-intercept form
The slope-intercept form of an equation of straight line is written as
y = mx +c
To write the equation, 2x+3y=24, in the slope-intercept form, we will make y the subject of the equation
[tex]2x+3y=24[/tex]
First, subtract 2x from both sides of the equation
That is,
[tex]2x -2x +3y = 24 -2x[/tex]
This becomes
[tex]3y = 24 -2x[/tex]
Now, divide both sides by 3
[tex]\frac{3y}{3} =\frac{24-2x}{3}[/tex]
∴ [tex]y = \frac{24}{3}-\frac{2x}{3}[/tex]
[tex]y = 8-\frac{2}{3}x[/tex]
In the slope-intercept form, we get
[tex]y = -\frac{2}{3}x+8[/tex]
Hence, the equation 2x+3y=24 in the slope-intercept form can be written as [tex]y = -\frac{2}{3}x+8[/tex]
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Translate the algebraic expression into a verbal expression. A/3 - 5b
Answer:
5 times a number subtracted from another number divided by 3.
Step-by-step explanation:
Solve for the value of s.
77°
(8s+5)
HELP PLS 20 POINTS
;w; can someone please help me... i have tried asking these before and people just give me a really confusing or incomplete answer.. please dont answer if you dont know the answer, if there is gonna be any links in your answer and/or its just gonna be random letters and not a complete answer
Answer:
Level 2:
45 x 45 = 2025
28 x 28 = 784
2025 + 784 = 2809
(sqrt)2809 = 53
53 units
Level 3:
(Start by graphing the coordinates)
Your shape should have one leg of 14 units, and one leg of 8 units.
14 x 14 = 196
8 x 8 = 64
196 + 64 = 260
(sqrt)260 = 16.1245155
(rounded to nearest tenth)
16.1 units
I`m not sure about the other two though, sorry :/
3. Using the Pythagorean theorem, x = 53 in.
4. 6, 9, and 11 does not form a right triangle because they are not a Pythagorean triple. i.e. 11² ≠ 9² + 6².
5. Using the distance formula, AB = 16.1 units
7. Height of the Pyramid using the Pythagorean theorem is: h = 5.2 units.
8. Length of diagonal = 10.2 units.
What is the Pythagorean Theorem?If c is the hypotenuse of a right triangle with a and b as its legs, the Pythagorean theorem states that c² = a² + b².
What is the Diagonal of a Rectangular Prism?Diagonal (d) = √(l² + h² + w²)
l = length
w = width
h = height
3. Find x using the Pythagorean theorem:
x = √(45² + 28²)
x = 53 in.
4. 6, 9, and 11 does not form a right triangle because they are not a Pythagorean triple. i.e. 11² ≠ 9² + 6².
5. Using the distance formula, find AB:
AB = √(5−(−3))² + (6−(−8))²
AB = √260
AB = 16.1 units
7. Height of the Pyramid using the Pythagorean theorem:
h = √(6² - 3²)
h = 5.2 units.
8. Diagonal of the Rectangular Prism:
Length of diagonal = √(l² + h² + w²) = √(8² + 5² + 4²)
Length of diagonal = 10.2 units.
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Kaj bought three pounds of strawberries for $7.20. What is the price, in dollars per ounce of strawberries?
Answer:
The amount per pound would be:
$2.40
Step-by-step explanation:
720 divided by 3 = 240
We can then conclude that:
$7.20 divided by 3 = $2.40
Have a great rest of your day
#TheWizzer
Answer:
0.15 dollars, of 15 cents (I believe)
Step-by-step explanation:
3 pounds, 16 oz per pound is 48 oz. 7.20 divided by 48 oz is 0.15, which should be equal to 15 cents. Hope this helps :)
Find the Surface of the prism 4in 10 in and 18in
Answer:
Step-by-step explanation:
total surface area = 584 m2
lateral surface area = 504 m2
top surface area = 40 m2
bottom surface area = 40 m2
A recipe for a cookie batch calls for 5/8 cup of flour. There are three and three-fourths cups of flour in a bag in the cupboard. How many batches of cookies can you make?
Answer:
So a batch is 5/8
There are THREE 3/4th cups of flour in the cupboard.
So 3 three fourths so basically
3/4 * 3 = 9/4 or
3/4 + 3/4 + 3/4 = 9/4
9/4 and each batch is 5/8.
9/4 ÷ 5/8 = 72/20 or 3 1/10
3 batches of cookies.
By the time the blizzard was over the temperature had dropped from
17°F to -6°F This was a drop of how many degrees?
Answer:
23
Step-by-step explanation:
To get to 17 degrees, you need to add 6 to -6 to get to 0.
And to get to 17 from 0, you need to add 17.
So then you add 6 and 17 together.
6+17=23
can someone help me with this math problem
Answer the one you would like. Thank you.
Answer: 2016 in^2
Step-by-step explanation:
3) Let's start with the taller rectangular prism. The height is 24", the width is 12", and the length is 12". The smaller rectangular prism is actually a cube because the height, width, and length are all 12". Just as a refresher, the surface area of an object is only the area of each outside face. For rectangular prisms, the surface area is 2(lh+wh+lw) (l=length, h=height, w=width). And for cubes, the surface area is 6s^2, where s is the side. 2(12*24+12*24+12*12) is equal to 1440 inches squared, however, half of one face is covered. This is the longest face shaded in dark green: 24" times 12", but because only half is showing, it is 24*12 divided by 2. This is equal to 144"; and you must subtract this from the entire surface area to account for that covered space. 1440-144 is 1296 inches squared. The cube is (12*12)(6) which is 864. But one whole side is covered, meaning you need to subtract 144 to have the surface area be 720 inches squared. 1296 plus 720 is 2016 inches squared. Decounting the half a side from the prism and one full side from the cube, there are only 10 and a half sides shown.
Hope this helps :)
HELP HELP HELP HELP HELP HELP
Answer:
x = 24°
Step-by-step explanation:
What do the sum of all angles in a triangle add up to?
The sum of all angles in a triangle add up to 180°.First, let's find the missing angle of the big triangle (the angle next to 111°).
94 + 41 = 135180 - 135 = 45°Now, we can find the value of x given the smaller triangle's angle.
x + 111 + 45 = 180x + 156 = 180x = 24Therefore, x = 24°.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
24 degrees
Step-by-step explanation:
Right corner angle
= 180 - 94 - 41
= 180 - 135
= 45 degrees
angle x
= 180 - 111 - 45
= 180 - 156
= 24 degrees
Write the equation of the line parallel to x = 5 that passes through (2, 7)
Answer:
Write the equation of the line parallel to x = 5 that passes through (2, 7)
if the measure of angle 4 is 55 what is the measure of angle 2
Answer:
No chart is provided
Step-by-step explanation:
ZN
is tangent to circle OO at point ZZ. If \text{m}\overset{\huge\frown}{ZMB} = 280^{\circ}m
ZMB
⌢
=280
∘
, find \text{m}\angle BZNm∠BZN.
Given tangent, ZN, to the circle and the arc [tex]\widehat{ZMB}[/tex] = 280°, we have that
the angle formed by the chord BZ and the tangent ZN, ∠BZN is 50°
Which method can be used to find ∠BZN?The given parameters are;
A tangent to the circle O = ZN
[tex]m \widehat{ZMB}} = \mathbf{280^{\circ}}[/tex]
Required:
Angle ∠BZN
Solution;
Please find attached the drawing of the circle and tangent
From the drawing, we have;
∠BOZ = 360° - 280° = 80°
ΔBOZ is an isosceles triangle, which gives;
∠BZO = ∠ZBO
[tex]\angle BZO = \dfrac{(180^{\circ}- 80^{\circ}) }{2} = \mathbf{50^{\circ}}[/tex]
∠OZN = 90° (by definition of a tangent)
∠OZN = ∠BZO + ∠BZN
∠BZN = ∠OZN - ∠BZO
Which gives;
∠BZN = 90° - 40° = 50°
The measure of angle ∠BZN = 50°Learn more about tangents to a circle here:
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21 is increased to 15
Answer:
36
Step-by-step explanation:
21+15 is 36 so there for u just add 15 to 21 giving you 36
Answer:
40%
Step-by-step explanation:
15 to 21;(21-15)x100=?;x 100;(21-15)x100=40%Paula's kitten weighs 3 1/2 pounds. Write this weight in the boxes using pounds and ounces.
Answer:
3 pounds and 8 ounces
Step-by-step explanation:
1 pound is 16 ounces, 1/2 pound is 8 ounces.
If you need further help, let me know!
-profparis
The students in Suzanne's school are painting a rectangular mural outside the building that will be 15 feet by 45 feet. Scale drawing of the mural is shown. The diagonal is approximately 6.3 units.Write the unit rate for the proportional relationship between lengths on the mural y and lengths in the scale drawing x.
Answer:
The dimensions on paper are 1.992ft by 5.976ft with a scale factor of 7.53
Step-by-step explanation:
The first step will be to find the diagonal of the rea life mural.
We can use Pythagoras' Theorem to do this.
Diagonal = [tex]\sqrt{15^2 +45^2 }[/tex] =47.43 feet.
Now we have the real-life diagonal, we will now relate the diagonal of the painting outside with the one on paper. We can do this by dividing the two diagonals.
This will be 47.43 / 6.3 units = 7.53.
The scale factor is 7.53
To get the dimensions of the length and the breadth on paper, we divide the outside dimensions by the scale factor.
This will be
Length = 15/ 7.53 = 1.992
Breadth = 45/7.53 = 5.976
Therefore, the dimensions on paper are 1.992ft by 5.976ft with a scale factor of 7.53
Simplify the following (12+7)-(2-23)
Answer:
40Step-by-step explanation:
Simplify the following (12+7)-(2-23)
(12 + 7) - (2 - 23) =
19 - (-21) =
19 + 21 =
40
Which number is closest to the CUBE ROOT of -205? *
-5.1
-5.5
o 5.9
-6.1
Answer:
-5.5
Step-by-step explanation:
Answer:
-5. 9
Step-by-step explanation:
[tex] \sqrt[3]{ - 205} = - 5.8963...... = approximately - 5.9[/tex]
Does a right triangle exist where sin A = sin B = cos A = cos B, where A and B are the two acute angles of the triangle? Provide evidence to support your conclusion, and if possible, find the measures of angles A and B.
Answer:
Step-by-step explanation:
When you list the trigonometic ratios for both acute angles in a right triangle, you notice some interesting developments.
Let's concentrate on sine and cosine:
Observation from the table above: notice1
In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B.
If ∠A and ∠B are the acute angles of a right triangle,
sin A = cos B
Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.
If we write, m∠B = 90º - m∠A (or m∠A = 90º - m∠B ), and we substitute into the original observation, we have:
notice4
If θ is substituted for m∠A , we establish the following relationship between sine and cosine:
sincosrule
The sine of any acute angle is equal to the cosine of its complement.
The cosine of any acute angle is equal to the sine of its complement.
Sine and cosine are called "cofunctions", where the sine (or cosine) function
of any acute angle equals its cofunction of the angle's complement.
FYI: What about tangent?
Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle. It is not, however, the same type of relationship that exists between sine and cosine.
The tangent of ∠A is the reciprocal (flip over) of the tangent of ∠B.
The angles being used in the following examples are acute angles.
ex1
If sin 30º = ½ and cos θ = ½,
find θ. Solution: Since both trig functions = ½,
30º and θ must be complementary.
θ = 60º
ex2
If sin(3x + 10)º = cos(x + 24)º,
find x. Solution: In order for the sine and cosine to be equal, the angles must be complementary.
3x + 10 + x + 24 = 90
4x + 34 = 90
4x = 56
x = 14
ex3
If sin(15º) = 0.26 and
cos (15º) = 0.97,
find sin(75º) and the cos(75º). Solution: The sine of an angle and the cosine of its complement are equal.
15º and 75º are complementary.
sin(75º) = cos(15º) = 0.97
cos(75º) = sin(15º) = 0.26
ex4
In right ΔABC, m∠C = 90º,
sin A = x + 0.1 and cos B = 2x - 0.4. Find x. Solution: If A and B are the acute angles of a right triangle, sin A = cos B.
x + 0.1 = 2x - 0.4
0.5 = x
Asap! I’ll mark you brainlest
What does how much money does he have before mean?
Add
Subtract
Divide
Multiply
Answer:
subtract? this is put together weird maybe add a screenshot so we know what to solve
Step-by-step explanation:
7. The total cost of producing 475 calculators was $12,825. What is the unit cost (that is, the cost of producing 1 calculator)?
Which expression is a monomial
Show the process also please!!
360 - 120 = 240
240 / 21 = 11.4
11.4cm
what is the factored form of x2-6x-16 ?
Answer:
(x + 2)(x - 8)Step-by-step explanation:
Factorize
x^2 - 6x - 16 =x^2 + 2x - 8x - 16 = x(x + 2) - 8(x + 2) =(x + 2)(x - 8)Could someone help me, please
Answer:
Q1: No solutions
Q2: x=2, y=-2
Q3: x=1, y=4
Step-by-step explanation:
Q1: Found out 0y = 18 which is impossible therefore no solution.
Q2:
In the first equation: [tex]2x - 4y = 12[/tex]
Let's express x in terms of y by changing the subject. Follow my steps.
[tex]2x = 12+4y[/tex]
[tex]x = \frac{12+4y}{2}[/tex]
Now let's put the x above into the second equation: [tex]-14x-4y=-20[/tex]
It becomes: [tex]-14(\frac{12+4y}{2})-4y=-20[/tex]. Follow my steps.
[tex]-7(12+4y)=-20+4y[/tex]
[tex]-84-28y=-20+4y[/tex]
[tex]-32y=64[/tex]
[tex]y=-2[/tex]
Put y = -2 into the first equation:
[tex]2x-4(-2)=12[/tex]
[tex]2x+8=12[/tex]
[tex]2x=12-8[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
Q3:
Multiply the first equation by 3 and the second equation by 7, so that both are 21x.
1st equation:
[tex]3(7x-3y)=3(-5)[/tex]
[tex]21x-9y=-15[/tex]
2nd equation:
[tex]7(3x+2y) = 7(11)[/tex]
[tex]21x+14y = 77[/tex]
We can now substract the 2nd equation with the 1st equation so that both 21x cancels out and only the variable y remains.
[tex]21x-9y-(21x+14y)=-15-77[/tex]
[tex]21x-9y-21x-14y=-92[/tex]
[tex]-23y=-92[/tex]
[tex]y=4[/tex]
Put y = 4 into the second equation to find x.
[tex]3x+2(4)=11[/tex]
[tex]3x+8=11[/tex]
[tex]3x=11-8[/tex]
[tex]3x = 3[/tex]
[tex]x=1[/tex]