the angles of a quadrilateral are 5x - 30°, 60° - x, 3x + 60° and 4x + 50°. Find the smallest of these angles?
The sum of all andles in quadrilateral is equal to 360°, so
[tex]5x - 30 + 60 - x + 3x + 60 + 4x + 50 = 360 \\ 11x = 220 \\ x = 20[/tex]
Now we need to put x into polynomials
1)
[tex]5 \times 20 - 30 = 70[/tex]
2)
[tex]60 - 20 = 40[/tex]
3)
[tex]3 \times 20 + 60 = 120[/tex]
4)
[tex]4 \times 20 + 50 = 130[/tex]
Answer: the smallest ahgle is 60-x
Which angles are alternate exterior angles.
Given the diagram below, find the measure in degrees of angle b & angle c
1) B= 68, C= 34
2) B= 68, C=68
3) B=34, C= 34
4) B=34, C=68
The measurements of the angles ∠ABD and ∠ACD will be 34° and 34°. Then the correct option is C.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The central angle is double the angle at the periphery that was subtended by the same chords.
Then the arc AD is double of angle ∠ABD.
∠ABD = arc AD / 2
∠ABD = 68° / 2
∠ABD = 34°
Similarly, the arc AD is double of angle ∠ACD.
∠ACD = arc AD / 2
∠ACD = 68° / 2
∠ACD = 34°
Thus, the measurements of the angles ∠ABD and ∠ACD will be 34° and 34°.
Then the correct option is C.
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A circle has a circumference of 25 meters. Find the length of an arc formed from a
central angle of 90°.
Answer:
If circumference = 25, then 90 degrees (one quarter of a circle) = 25 / 4 = 6.25 meters.
Step-by-step explanation:
Part of the graph of the function f(x) = (x + 4)(x - 6) is shown below. which statement about the function are true? Select two options. - The vertex of the function is at (1,-25) - The Vertex of the function as at (1,-24) - The graph is increasing only on the interval-4< x < 6. - The graph is positive only on one interval, where x < -4. - the Graph is negative on the entire interval -4 < x < 6.
Answer:
Hya, The vertex of the function is at (1,-25) and the Graph is negative on the entire interval -4 < x < 6.
Step-by-step explanation:
1. the vertex of the function:
f(x)= (x + 4)(x - 6) = x^2 - 2x - 24
x₀= 2/2= 1 y₀= 1^2 - 2*1 - 24= -25
(1; -25)
2. the Graph is negative on the entire interval -4 < x < 6
Answer:
The vertex of the function is at (1,–25).
The graph is increasing only on the interval −4< x < 6.
Step-by-step explanation:
A and C on edg
The length of the minute hand of a clock is
14 inches. What is the length of the path traced
by the outer tip of the minute hand in one
hour? Use 22
7 for p.
Answer:
Step-by-step explanation:
Given
Length of the minute hand = 14 inches
Time = 1 hour
Required
Length of the path traced in 1 hour
For, the minute hand to have completer an hour, this means it completes a cycle;
1 cycle is equivalent to 1 complete rotation;
So, basically the question implies that; the circumference of the complete rotation be solved for;
To solve for this; we make use of the circumference formula;
[tex]C = 2\pi r[/tex]
Where
C represents the circumference
r represents the radius or the length of the minute hand
[tex]\pi = \frac{22}{7}[/tex] --- This is given from the question;
By substitution, we have
[tex]C = 2 * \frac{22}{7} * 14[/tex]
[tex]C = \frac{2 * 22 * 14}{7}[/tex]
[tex]C = \frac{616}{7}[/tex]
[tex]C = 88 inches[/tex]
Hence, the length of the path traced is 88 inches
Which would result in the largest amount of money?!
35% of $1,000
10% of $375
7% of $5,200
50% of $640 plus 25% of $160
answer quickly and correctly and I will mark you brainliest!
Answer:
c 364
Step-by-step explanation:
this is the correct answer because the rest are lower answers
Answer:
the answer is 7% of 5,200.
Step-by-step explanation:
35% of 1000 is 350
10% of 375 is 37.5
07% of 5,200 is 364
and 50% of 640 (320) plus 25% of 160 (40) is 360
hope this helps!
Determining the Vertex of a Parabola from Its Graph
On a coordinate plane, a parabola opens up with solid circles along the parabola at (negative 6, 5), (negative 5, 0), (negative 4, negative 3), (negative 3, negative 4), (negative 2, negative 3), (negative 1, 0), (0, 5).
What is the vertex of the parabola in the graph?
(
,
)
Answer:
(-3, -4)
Step-by-step explanation:
The solid circles along the parabola are:
(-6, 5), (-5, 0), (-4, -3), (-3, -4), (-2, -3), (-1, 0), (0, 5).
Although on observation, the minimum point of y occurs at (-3, -4), we can also confirm through the function.
The x-intercept of the parabola are -5 and -1.
x=-5 or x=-1
x+5=0 or x+1=0
(x+5)(x+1)=0
[tex]x^2+5x+x+5=0\\x^2+6x+5=0[/tex]
The Vertex of the equation occurs at the axis of symmetry, [tex]x=-\dfrac{b}{2a}[/tex]
In [tex]f(x)=x^2+6x+5, a=1, b=6[/tex]
Axis of Symmetry, [tex]x=-\dfrac{6}{2}=-3[/tex]
[tex]f(-3)=(-3)^2+6(-3)+5=9-18+5=-4[/tex]
Therefore, we can confirm that the vertex is (-3,-4) as stated earlier.
A company wants to increase the 10% peroxide content of its product by adding pure peroxide (100% peroxide). If x liters of pure peroxide are added to 100 liters of its 10% solution, the concentration, C, of the new mixture is given by the formula below. How many liters of pure peroxide should be added to produce a new product that is 70% peroxide? C= (x + 0.1(100))/(x +100)
Answer:
200 liters.
Step-by-step explanation:
To solve this, let's first set C in our equation to .7, since that is the concentration we are aiming for.
.7= [tex]\frac{(x+0.1(100))}{x+100}[/tex]
Next, we can simply this equation further:
.7= [tex]\frac{(x+10)}{x+100}[/tex]
We can multiply both sides by the denominator, resulting in:
.7x+70= x+10
Finally, continue simplifying to solve for x:
60= .3x
x= 200 liters.
what is the area of a pentagon with an apothem of 12 and side length of 17.4
Answer:
522
Step-by-step explanation:
For an n-sided polygon, with apothem a, and side s, the area is
A = ans/2
A = (12)(5)(17.4)/2
A = 522
To find the area of a triangle, you can use the expression b times h divided by 2, where b is the base of the triangle and h is it’s height. What is the area of a triangle with a base of 8 and a height of 4?
Answer:
16 sq. units
Step-by-step explanation:
The formula for the area of a triangle:
A = 1/2bhIf base and height are known as:
b = 8 units and h = 4 unitsThen the area is:
A = 1/2*8*4 = 16 sq. unitsWhat is the approximate circumference of the circle shown below?
Answer:
A
Step-by-step explanation:
to find the circumference of a circle, u multiply the diameter by pi. pi is approximately 3.14. 12.2 times 3.14 is 38.308. rounded to the nearest tenth it is 38.3 :)
Natasha’s family has advised her not to depend completely on the insurance that her employer provides. Natasha now plans to independently obtain property and casualty insurance, auto insurance, and other insurance related to her personal life. What are the two ways in which she can accomplish her goal?
A. by seeking help from the human resource department of her company
B. by asking her family members to share their insurance with her
C. by hiring a local agent or broker who is familiar with her needs
D. by letting her employer-based life insurance and health insurance coverage lapse
E. by registering on the website of a national insurance company
Answer:
C. by hiring a local agent or broker who is familiar with her needs
and
E. by registering on the website of a national insurance company
Step-by-step explanation:
Just got this right on Plato :)
To independently obtain additional insurance, Natasha has two main options: hiring a local insurance agent or broker for personalized service, or registering on the website of a national insurance company for convenience and direct-purchase options.
Explanation:Natasha can accomplish her goal of obtaining additional insurance coverage independently from her employer by following two main paths:
C. by hiring a local agent or broker who is familiar with her needs, orE. by registering on the website of a national insurance company.By consulting a local insurance agent or broker, she can receive personalized advice and find coverage that fits her specific situation.
On the other hand, registering on the website of a national insurance company allows her the convenience to compare different plans and sign up for insurance that she can directly purchase.
Doing either will help her cover personal assets and health beyond what her employer provides without affecting her existing employment-based insurance coverage. It's important for her to assess her individual needs, risk factors, and financial situation when choosing the best insurance plans for her lifestyle.
Complete the statements about the graph.
units.
The length of the transverse axis is
is a focus of the hyperbola.
A vertex of the hyperbola is located at
Y
Answer:
16
(0,17)
(0,8)
Step-by-step explanation:
i got it right
The length of the transverse axis is the distance between the vertices of the hyperbola. A focus of the hyperbola is a fixed point from which distances to any point on the hyperbola have a constant difference. A vertex of the hyperbola is where it intersects its transverse axis.
Explanation:When analyzing graphs, it is crucial to understand the properties of the figures involved. In this case, we are discussing a hyperbola, which is a set of all points where the difference in the distances from two fixed points, called foci, is constant.
The length of the transverse axis of a hyperbola is the distance between its vertices. For an ellipse as shown in Figure 3.4 (b), the distance between the two vertices on the major axis is 2a, where a is the length of the semimajor axis. However, in the case of a hyperbola, the transverse axis would correspond to the axis that goes through the two vertices of the hyperbola.
A focus of the hyperbola is one of the two fixed points from which the difference in distances to any point on the hyperbola is constant. It is typically denoted as (h ± c, k) in the Cartesian coordinate system, where (h, k) is the center of the hyperbola and c is the distance from the center to each focus.
A vertex of the hyperbola is located at the point on the graph where the hyperbola intersects its transverse axis. This can be expressed as (h ± a, k) for a horizontal hyperbola or (h, k ± a) for a vertical hyperbola, where (h, k) is the center of the hyperbola and a is the length of the semimajor axis.
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The hu family goes out for lunch and the price of the meal is $45 the sales tax on the meals is 6% and the family also leaves a 20% tip on the pretax amount what is the total cost of the meal
Answer:
$56.7
Step-by-step explanation:
For this, you need to find out the tip and the tax.
45 x .06 = 2.7
45 x .2 = 9
After you find out that, add them together and that will be the total cost.
45 + 2.7 + 9 = 56.7
Feel free to let me know if you need more help. :)
Use the order of operations to find the value of the expression.
2+3*16-2*21-3
O A.5
O B.14
O C.35
O D.44
Answer:A. will be your answer
Step-by-step explanation:
By using the order of operations to find the value of the expression 2 + 3 × 16 − 2 × 21 − 3, we get; A. 5
What is BODMAS?The order is called BODMAS which stands for Bracket, Of, Division, Multiplication, Addition, Subtraction.
We need to use order of operations to solve the problem;
2 + 3 × 16 − 2 × 21 − 3
we will first carry out multiplication to get;
= 2 + 48 - 42 - 3
Next in addition to getting;
= 50 - 42 - 3
= 5
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Which equation is equivalent to 4^x+3=64
A) 2^x+6 = 2^4
B)2^2x+6 = 2^6
C) 4^2x+6 = 4^2
D)4^x+3 = 4^6
IF SOMEONE ANSWERS CORRECTLY WITHIN 5 MINUTES THEY WILL GET BRANLIEST ANSWER
An explosion causes debris to rise vertically with an initial velocity of 144 feet per second. The function s left parenthesis t right parenthesis equals negative 16 t squared plus 144 t describes the height of the debris above the ground, s(t), in feet, t seconds after the explosion. What is the instantaneous speed of the debris when it hits the ground?
Answer:
160ft
Step-by-step explanation:
please i really need help
Answer:
B
Step-by-step explanation:
25x² - 144 ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b), thus
25x² - 144
= (5x)² - 12²
= (5x + 12)(5x - 12) → B
Answer:
B) ( 5x + 12 ) ( 5x - 12 )
Step-by-step explanation:
Since we have options we could try expanding all of them out.
A) ( 12 + 5x ) ( 12 - 5x )
144 - 60x + 60x - 25x² = 144 - 25x²
That's not the answer we are looking for so we cross out "a" as an option
B) ( 5x + 12 ) ( 5x - 12 )
25x² - 60x + 60x - 144 = 25x² - 144
This is the answer which we are looking for so B is the answer
see picture^
can someone pls help me with this question, i will give brainliest to the first answer that’s right
Answer:
No.
Step-by-step explanation:
First class section seats: 5/7 = 10/14 so 10 seats are being used.
Business: 5/16 = 20/64, 20 seats are being used.
Economy: 5/9 = 60/108, 60 seats are being used.
10 + 20 + 60 = 90
108 + 64 + 14 = 186
90/186 is less than 1/2, because 1/2 = 93/186
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 18, 3, 0, 3, 6, 3.
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
Answer:
[-1, 1]
Step-by-step explanation:
Comparing each table value to the one before, we find the function to be increasing on the interval [-1, 1].
__
The graph in the second attachment shows that integer interval to be the only one where the function is increasing.
Answer:
-1,1
Step-by-step explanation:
time for learning
At a cost restaurant the cost for a hot dog and a soft drink is $2.10. The cost for two hot dogs and three soft drinks is $5.15. Determine the cost of a soft drink
Answer:
The cost of soft drink is $0.95
Step-by-step explanation:
Let the cost of hot dog be x
Cost of 2 hot dogs = 2x
Let the cost of soft drink be y
Cost of 3 soft drinks = 3y
At a cost restaurant the cost for a hot dog and a soft drink is $2.10.
So, x+y=2.10
The cost for two hot dogs and three soft drinks is $5.15
So, 2x+3y=5.15
Plot the lines on the graph:
x+y=2.10 --Purple line
2x+3y=5.15 --- Black Line
Intersection point =(x,y)=(1.15,0.95)
Hence The cost of soft drink is $0.95
Consider two circular swimming pools. Pool A has a radius of 16 feet, and Pool B has a diameter of 9.94 meters. Complete the description for which pool has a greater circumference. Round to the nearest hundredth for each circumference. 1 foot ≈ 0.305 meters
Answer:
Pool B has the greater circumference.
Step-by-step explanation:
Pool A has a radius of 16 feet, and Pool B has a diameter of 9.94 meters.
We want to see which pool has a greater circumference.
The circumference of a circle is the distance around a circle or the total length of a circle, and it is given as:
[tex]C = 2\pi r[/tex]
where r = radius of the circle
So that our comparison can be accurate, let us put the dimensions of both pools in a single unit, metre.
The radius of pool A is 16 feet.
1 foot = 0.305 metres
16 feet = 4.88 metres
The radius of pool A in metres is 4.88 metres
CIRCUMFERENCE OF POOL A
[tex]C = 2 * \pi * 4.88 = 30.66 m[/tex]
CIRCUMFERENCE OF POOL B
[tex]C = 2 * \pi * 9.94 = 62.45 m[/tex]
As we can see, pool B has the greater circumference.
Answer:
Answer is on the picture below
Step-by-step explanation: the one that only says pool is pool B
Thank you! :)
Nour and Rana are shopping for a Christmas tree. They are deciding between 2 different types of trees (real and fake) and 4 colors for the ornaments (white, silver, gold, and purple). They each created a display to represent the sample space of randomly picking a type of tree and a color for the ornaments. Whose display correctly represents the sample space? (Choice A) Nour only (Choice B) B Rana only (Choice C) C Both (Choice D) D Neither
Answer:
Both
Step-by-step explanation:
Choose the correct elevation for the peak shown.
Answer:600
Step-by-step explanation:
it’s the highest point
what is the y- intercept of the line?
Answer:
Your Y-Intercept should be -2
Step-by-step explanation:
You always need to look at where the line starts according to the coordinate when X = 0, or when the dot is in the very middle line.
Therefore, we can see that it starts at "down two", also known as "-2"
Answer:
it is 2
Step-by-step explanation:
to find the Y-intercept of a line, first u should find the slope intercept form
slope intercept form : y=mx+b
m=slope
b= y-intercept
first u should find the slope, so pick two points from the line and write them in a form of y2-y1/x2-x1
point 1: (1,0)
point 2: (2,2)
0-2/2-1=-2/1
m=-2
now pick one of the two points and replace it in the equation with the slope
0=-2(1)+b
solve for b
0=-2+b
add 2 on both sides
b=2
Lance the alien is 5 feet tall. His shadow is 8 feet lopg.
5 ft
8 ft
32 it
At the same time of day, a tree's shadow is 32 feet long. What is the height of the tree?
Answer:
20 ft
Step-by-step explanation:
The 2 triangles are similar, thus the ratios of corresponding sides are equal.
let h be the height of the tree, then
[tex]\frac{h}{5}[/tex] = [tex]\frac{32}{8}[/tex] = 4 ( multiply both sides by 5 )
h = 20
The height of the tree is 20 ft
The height of the tree that both triangles are similar to is 20 feet.
What is symmetry?If two figures look an exact shape but their size could be small or big then both figures are called similar figures.
When anything has identical pieces facing one another or revolving around an axis, it is said to be symmetrical.
As per the given two triangles,
Let's say the height of the tree is h.
By similar triangle property
h/32 = 5/8
h = (5/8)32
h = 5 x 4 = 20 feet
Hence "The height of the tree that both triangles are similar to is 20 feet".
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Landon left a garbage can on the lawn and the grass underneath it died. The diameter of
the can is 54 centimeters. What is the area of the grass that died? Use 3.14 for pi.
Answer:
The area of the grass that died is 2,289.06 cm²
Step-by-step explanation:
In order to calculate the area of the grass that died, we need to calculate the area of the bottom of the trash can. Since it's a circular shape it's area is given by:
area = pi*r²
Where r = d/2, therefore:
r = 54/2 = 27 cm
Applying this data to the formula, we have:
area = pi*(27)² = 2,289.06 cm²
The area of the grass that died is 2,289.06 cm²
Can you do this problem and show work
Answer:
[tex]2(3x+5)+5(2x+2)[/tex]
[tex]6x+10+5\left(2x+2\right)[/tex]
[tex]6x+10+10x+10[/tex]
[tex]16x+20[/tex]
[tex]8(3x+2)+7(x+3)[/tex]
[tex]24x+16+7x+21[/tex]
[tex]31x+37[/tex]
¿Cuál es el valor de i51
?
A.
−1
B.
−i
C.
1
D.
i
Answer: Option B.
Step-by-step explanation:
We want to find the value of i^51
We know that
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
and it repeats with a period of 4, so i^5 = i^(1 + 4) = i^1= i, and so on.
so we can write it as:
x + n*4 = 51
where n is an integer number, and x is a number between 1 and 4.
clearly n must be an odd number, so we can try:
if x = 1.
1 + n*4 = 51
n*4 = 50
n = 50/4 = 12.5
This is not the solution for x, because n must be an integer number.
Now suppose x = 3.
3 + 4*n = 51
4*n = 48
n = 48/4 = 12
Then x is equal to 3, this means that:
i^51 = i^3*i^4*12 = i^3 = -i
The correct option is B