We see that Triangle ABC is an isosceles triangle which means:
Sides BA and BC are equal in lengthAngle BAC and BCA are equalWe see that Angle BCD and Angle BCA are on a straight line, which means that both of the angles' measures are equal to 180 degrees
--> in equation form:
Angle BCD + Angle BCA = 180
118 + Angle BCA = 180
Angle BCA = 62 degrees
Since Angle BCA and BAC are equal, then Angle BAC or Angle A in this case is 62 degrees
Hope that helps!
What is the sale price of jeans which regularly cost $32, but now are 10% off?
Answer:
$28.80
Step-by-step explanation:
32 x 0.1 = 3.2
32 - 3.2 =28.8
Hope this helps :)
Answer:
$28.8
Step-by-step explanation:
10% of 32 is 3.2
32 - 3.2 = 28.8
If (x − 5) is a factor of the polynomial function f(x) = 3x2 − 23x + 40, which of the following is another factor?
Answer:
3x-8
Step-by-step explanation:
Use synthetic division:
5 | 3 -23 40
____ 15 -40_
3 -8 | 0
Hence, another factor of the polynomial is 3x-8
HELP ASAP
I WILL GIVE BRAINIST
answer:
jesus know the answer
Lacie bought a $20 shirt that was marked down 30%. what did she pay after tax of 6% was added to the price of the shirt?
Answer:
14.84
Step-by-step explanation:
20*(6%+1)*(1-30%)
20*(0.06+1)*1-0.3)
20*1.06*0.7
14.84
A company produces circular drink coasters. the equation x2 y2 = 18.0625, with units in inches, represents the size of a coaster. each coaster is cut from a square piece of cardboard. what is the minimum possible area of each cardboard piece? 4.25 in2 8.5 in2 18.0625 in2 72.25 in2
The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
A company produces circular drink coasters. the equation which represents the size of a coaster is,
[tex]x^2+ y^2 = 18.0625[/tex]
The units are in the inches. This equation can be written as,
[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]
Compare it with the equation of the circle, we get,
[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]
The radius of the circular coaster is 17/4. The diameter of it is,
[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]
Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.
[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]
The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,
[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]
Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
Learn more about the equation of circle here;
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In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many right-handed females as there are right-handed males. There are a total of 204 males and 348 females in the town.
Let x represent the number of left-handed females, and let y represent the number of right-handed males. Write a system of equations to represent the situation. What is the value of x, the number of left-handed females?
6
24
96
108
Answer:
(b) 24
Step-by-step explanation:
The given variable definitions and the given relationships let us write these statements:
LH males = 4 × LH females = 4x
RH females = 3 × RH males = 3y
LH males + RH males = 204 = 4x +y
RH females + LH females = 348 = 3y +x
Your favorite method of solving equations of this sort can tell you ...
(x, y) = (24, 108)
There are 24 left-handed females.
__
Additional comment
Other numbers involved here are ...
y = 108 . . . . right-handed males
204-108 = 96 . . . . left-handed males (=4×24)
348-24 = 324 . . . . right-handed females (=3×108)
__
If you want to solve the equations by hand, you can use substitution for y to get an equation in x:
3(204 -4x) +x = 348 ⇒ -11x = -264 ⇒ x = 24
A husband and wife are building a tiny house for a vacation getaway, and they want to measure the height of the roof of the house to see if they will be able to have a bedroom on the second floor. One side of the house is 18 ft long and the slant height of the roof along this side is 13 ft. The point on the roof's peak is above the center of the house. What is the height of the roof of the house? Round your answer to the nearest hundredth. Question 4 options: 9.38 ft 11.28 ft 15.21 ft 9.4
By using a right triangle as a model, we will see that height of the roof is 9.38 ft.
What is the height of the roof of the house?The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft
We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:
X^2 + (9ft)^2 = (13 ft)^2
X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft
So the height of the roof is 9.38 ft.
If you want to learn more about right triangles, you can read:
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What does the 6 in 2/6 mean?
Hey there!
Here we have a fraction
2/6.
The 2 is the numerator, and 6 is the denominator.
How to remember where the numerator and the denominator is?
Well, please remember the following:
The Denominator is Down
Hence, 6 is the denominator of this fraction.
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
Write -1.7 repeating as a fraction
Answer:
-1 7/10
Step-by-step explanation:
Hope that helps!!!
find ml 2x+5 5x-4 Brainliest HURRY RN
Answer:
11
Step-by-step explanation:
5x + -4 = 2x + 5
-2x +4 -2x +4
3x = 9
x = 3
5(x) - 4 = ML
5(3) - 4 = ML
15 - 4 = ML
11 = ML
Identify the value of y.
-6×2×9y = 7y-4+4-690
Hey there!
-6×2×9y = 7y-4+4-690
=> Let's solve your equation step-by-step.
(((−6)(2))(9))(y)=7y−4+4−690
Step 1: Simplify both sides of the equation.
(((−6)(2))(9))(y)=7y−4+4−690
−108y=7y+−4+4+−690
−108y=(7y)+(−4+4+−690)(Combine Like Terms)
−108y=7y+−690
−108y=7y−690
Step 2: Subtract 7y from both sides.
−108y−7y=7y−690−7y
−115y=−690
Step 3: Divide both sides by -115.
−115y/−115 = −690/−115
y=6
Answer:
y=6
Therefore, the value of y = 6
Answer:
y=6
Step-by-step explanation:
(((−6)(2))(9))(y)=7y−4+4−690
−108y=7y+−4+4+−690
−108y=(7y)+(−4+4+−690)
−108y=7y+−690
−108y=7y−690
Subtract 7y from both sides.
−108y−7y=7y−690−7y
−115y=−690
Step 3: Divide both sides by -115.
−115y -690
−115 -115
y=6
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Hi! Im stuck on this question please help, thanks
Answer:
I guess it is 43.57 Hope it helps!!!
Find the domain over which the function y = x + 6x is monotonic increasing.
Answer:
x > -3
[tex]\sf (-3, \infty)[/tex]
Step-by-step explanation:
Domain: input values (x-values)
Monotonic increasing: always increasing.
A function is increasing when its graph rises from left to right.
The graph of a quadratic function is a parabola. If the leading term is positive, the parabola opens upwards. The domain over which the function is increasing for a parabola that opens upwards is values greater than the x-value of the vertex.
Vertex
Standard form of quadratic equation: [tex]\sf y=ax^2+bx+c[/tex]
[tex]\textsf{x-value of vertex}=\sf -\dfrac{b}{2a}[/tex]
Given function:
[tex]\sf y=x^2+6x[/tex]
Therefore, x-value of function's vertex:
[tex]\sf \implies x= -\dfrac{6}{2}=-3[/tex]
Final Solution
The function is increasing when x > -3
[tex]\sf (-3, \infty)[/tex]
Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town. He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below. According to this information, what would be the best estimate for Sam to quote as expected profits in the next year in his new business plan? Business Year Net Profit 1 $43,502. 25 2 $47,417. 45 3 $51,685. 02 4 $56,336. 68 5 $61,406. 98 a. $66,477. 28 b. $66,933. 60 c. $72,003. 91 d. $72,957. 63.
Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.
What is net profit?Net profit is the amount of a business earn after deducting all the expenditure over it.
Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town.
He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below.
Business Year Net Profit 1 $43,502.25 2 $47,417.45 3 $51,685.02 4 $56,336.68 5 $61,406.98Using the regression graph, the quadratic equation we get for this data as,
[tex]y=192.4493x^2+3318.1733x+39998.214[/tex]
For the 6 year value,
[tex]y=192.4493(6)^2+3318.1733(6)+39998.214\\y\approx 66835.43[/tex]
This value is much near to the option b which is $66,933.60.
Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.
Learn more about the Net profit here;
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Draw a number line to represent the street sign below
1) the height is 11 ft
2) base is 9 in and the height is 3 in
I just need to know the area
1. All 4 sides are the same length
Area = 11 x 11 = 121 square ft.
2. area = 9 x 3 = 27 square in.
marked price an article is 20% above its cost price. it is sold for rs 1100 at 10% profit find its marked price
Hey there!
Marked price (MP) = 1100 + Cost price (CP) ----(1)
If the watch was sold at discount of 20%, profit = Rs. 400
⇒ Selling price = MP - 20% of MP = 0.8MP
Also, Selling price = CP + 400
⇒ CP + 400 = 0.8MP
Substituting from (1),
⇒ CP + 400 = 0.8(1100 + CP)
⇒ CP + 400 = 880 + 0.8CP
⇒ 0.2CP = 480
⇒ CP = Rs. 2400
∴ To earn a profit of 30%, Selling price = 2400 + 30% of 2400 = 2400 + 720 = Rs. 3120
How much of a radioactive substance must be presented to decay to 80 grams in 12 years if the half-life of the substance is 7.6 years?
Answer:
Radioactive in half life is 51gram
Step-by-step explanation:
80grams:12years
X :7.6years
12x÷x=x
7.6×80÷12=51gram
Answer:
239 grams.
Step-by-step explanation:
Half life t(1/2) = ln 2 / k
So 7.6 = ln 2 / k
k = ln 2 / 7.6 = 0 0901204
N = No e^-kt
So after 12 years
80 = No / e^(-0.0901204*12)
No = 80 / e^(-0.0901204*12)
= 239.
Find the 53rd multiple of 62, if the 54th multiple is 3348.
Answer:
[tex]\displaystyle 3286[/tex]
Explanation:
Just multiply 62 and 53 to get 3286.
I am joyous to assist you at any time.
Please Help! will give brainlest!
Answer:
No, because triangle XYZ is not a right triangle.
Step-by-step explanation:
SOHCAHTOA (sin, cos, tan) can only work on right triangles. If a triangle is not a right triangle, you cannot use sin cos tan on it. This triangle is not a right triangle, so this is why you cannot fin the tangent ratio.
Erik rides his motorbike 26/23 miles in 23 hour. What is Erik’s average speed in miles per hour?
Answer:
Average speed = 40 mph.
Step-by-step explanation:
A board game that normally costs $30 is on sale for 25 percent off. What is the sale price of the game?
$22.50
$27.50
$32.50
$37.50
Answer:
22.50
Step-by-step explanation:
25% of 30 is 7.50
30-7.50 is 22.50
Answer: A: $22.50
Step-by-step explanation:
The original price of the game, $30, is 100%.
If the game if 25% off, then it will be, (100 - 25), 75% of its original price.
All we need to do is 75% x 30:
0.75 x 30 = 7.5 x 3 = $22.50
So your answer is A: $22.50
what is the slope-intercept form of the equation of the line that contains the points (-3,-3) and (4,5)
Answer:
[tex]y=1.14x+0.420[/tex]
Step-by-step explanation:
Given the following question:
Point A = (-3,-3) = (x1, y1)
Point B = (4, 5) = (x2, y2)
To write the points in slope intercept form we must first calculate the slope using rise over run. Once we have the slope, we substitute the values into the formula for slope intercept which is y = mx + b and then solve for b to have our answer.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{5--3}{4--3} =\frac{8}{7}[/tex]
[tex]8\div7=1.14[/tex]
[tex]m=1.14[/tex]
Now that we have the slope substitute the values:
[tex]y=mx+b[/tex]
[tex]y=-3[/tex]
[tex]m=1.14[/tex]
[tex]x=-3[/tex]
[tex]-3=1.14(-3)+b[/tex]
[tex]1.14\times-3=-3.42[/tex]
[tex]-3=-3.42+b[/tex]
[tex]-3.42+3.42=0[/tex]
[tex]-3+3.42=0.42[/tex]
[tex]0.42=b[/tex]
[tex]b=0.42[/tex]
[tex]y=1.14x+0.420[/tex]
Your answer is "y = 1.14x + 0.420."
Hope this helps.
Which equation can be used to calculate the surface area of the triangular prism net show below? The net of a rectangular prism. The rectangular sides are 10 centimeters by 13 centimeters, 10 centimeters by 12 centimeters, and 10 centimeters by 5 centimeters. The triangular sides have a base of 5 centimeters and height of 12 centimeters. [Not drawn to scale] Surface Area = (one-half) (5) (12) (5) (10) (12) (10) (13) (10) Surface Area = (one-half) (5) (13) (one-half) (5) (13) (13) (10) (12) (10) Surface Area = (2) (5) (13) (5) (10) (13) (10) (12) (10) Surface Area = (one-half) (5) (12) (one-half) (5) (12) (5) (10) (12) (10) (13) (10).
The [tex]13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12[/tex] equation can be used to calculate the surface area of the triangular prism.
It is given that the triangular prism net showing in the figure with dimensions.
It is required to find which equation can be used to find the surface area of the triangular prism net.
What is surface area?It is defined as the area of 3-dimensional geometry surfaces area sum which is occupying the outer area of the object.
We know the area of a rectangle = length × width
Area of the top rectangle = 13×10
Area of the middle rectangle = 12×10
Area of bottom rectangle= 5×10
The formula for finding the area of a triangle:
[tex]\rm A=\frac{1}{2} \times bh[/tex]
Area of right triangle = [tex]\rm \frac{1}{2} \times 5 \times12[/tex]
Area of left triangle = [tex]\rm \frac{1}{2} \times 5 \times12[/tex]
The surface area = Area of top+ Area of middle+ Area of bottom+ Area of
a right triangle+ Area of the left triangle
[tex]=13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12[/tex]
Thus, the [tex]13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12[/tex] equation can be used to calculate the surface area of the triangular prism.
Learn more about the surface area here:
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Is the following function even, odd, or neither f(x)=x^3/x+1
Answer: Odd
Step-by-step explanation:
Odd functions are functions where the exponent of the leading term is odd. In this case, the exponent of 3 is odd, so the function is odd.
3x - 12y = 6
x - 4y = 2
solve by elimination
3x-12y=6
x-4y=3--(1)x-4y=2--(2)Lets convert to slope intercept form
4y=x-34y=x-2Slopes are equal so lines are parallel
Hence no solutions
7x+ 8=29 how to solve it
Answer:
the correct answer is x = 3
Step-by-step explanation:
you solve this by moving all the terms that dont contain x to the right side and solve the equation.
hope this helps
have an awesome day -TJ
pls mark brainliest if this helps you :)
Solve: log2(3x 8) = 5 which is an equivalent equation? 25 = 3x 8 52 = 3x 8 25 = [log2(3x 8)]2 52 = [log2(3x 8)]5
The value of the equivalent equation will be 32=3x+8
What will be the value of x?It is given in the question that
[tex]\rm Log_2(3x+8)=5[/tex]
Now from the antilog property property
[tex]\rm x=Log_by[/tex] can be written as below
[tex]b^x=y[/tex]
So the value of [tex]\rm Log_2(3x+8)=5[/tex] will be
[tex]2^5=3x+8[/tex]
[tex]3x+8=32[/tex]
Thus the value of the equivalent equation will be 32=3x+8
To know more about Antilog property follow
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Answer:
I did it on edgeinuity
Step-by-step explanation:
factorise: 6x^2 – 5 x – 6
Step-by-step explanation:
I think it will help you.
Look at the example
Let's use mid-term splitation
[tex]\\ \rm\rightarrowtail 6x^2-5x-6[/tex]
[tex]\\ \rm\rightarrowtail 6x^2+4x-9x-6[/tex]
[tex]\\ \rm\rightarrowtail 2x(3x+2)-3(3x+2)[/tex]
[tex]\\ \rm\rightarrowtail (2x-3)(3x+2)[/tex]
Plot the points A(7,1), B(-2, 3), C(1, -7) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a parallelogram.
(Plotting point D is optional.)
A B
D C
vectors
AB = DC
AB (-2-7 ; 3-1) => AB (-9 ; 2)
DC (1-x : -7-y)
1 - x = -9 => x = 10
-7-y = 2 => y = -9
D(10 ; -9)
Answer:
D = (10, -9)
Step-by-step explanation:
If ABCD is a parallelogram, then AB = DC and BC = AD
Therefore,
[tex]\sf x_A-x_B=x_D-x_C[/tex]
[tex]\sf \implies 7-(-2)=x_D-1[/tex]
[tex]\sf \implies x_D=10[/tex]
[tex]\sf y_A-y_B=y_D-y_C[/tex]
[tex]\sf \implies 1-3=y_D-(-7)[/tex]
[tex]\sf \implies y_D=-9[/tex]
Therefore, D = (10, -9)