[tex]\\ \sf\longmapsto 14.3-4.1[/tex]
[tex]\\ \sf\longmapsto \dfrac{143}{10}-\dfrac{41}{10}[/tex]
[tex]\\ \sf\longmapsto \dfrac{143-41}{10}[/tex]
[tex]\\ \sf\longmapsto \dfrac{102}{10}[/tex]
[tex]\\ \sf\longmapsto 10.2[/tex]
The length of a rectangular photo is 1 centimeter less than three times its width. If the area of the photo is 102 square centimeters, find the length and width of the
photo.
The length is
and the width is
(Type whole numbers.)
Answers:
Length = 17Width = 6======================================================
How to get those answers:
Let w be the unknown width in centimeters. This variable is some positive real number. This means w > 0 which will be useful later.
The length is "1 cm less than 3 times its width" and it tells us the length is defined by the expression 3w-1. Whatever w is, we triple it to get 3w and then subtract 1 to get the final length.
Multiply the length and width to get the area 102
length*width = area
(3w-1)*w = 102
3w^2-w = 102
3w^2-w-102 = 0
We could guess and check our way to factoring this, but that's not very efficient. The quadratic formula is the better option. It may seem a bit messy, but it's a more direct path that doesn't involve guessing.
[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-102)}}{2(3)}\\\\w = \frac{1\pm\sqrt{1225}}{6}\\\\w = \frac{1\pm35}{6}\\\\w = \frac{1+35}{6}\ \text{ or } \ w = \frac{1-35}{6}\\\\w = \frac{36}{6}\ \text{ or } \ w = \frac{-34}{6}\\\\w = 6\ \text{ or } \ w \approx -5.667\\\\[/tex]
We ignore the second solution (w = -5.667 approximately) because we stated earlier that w > 0. In other words, a negative length does not make sense, so that's why we ignore it.
-----------------
If w = 6 cm is the width, then 3w-1 = 3*6-1 = 18-1 = 17 cm is the length.
Note that length*width = 17*6 = 102 which is the proper area we want. This confirms the answers.
HELP ME PLEASE ASAP! Zoe is making a quilt. The ratio of red squares to green squares is 2 to 3. She uses a total of 55 squares. How many green squares does she use?
Answer:
33
Step-by-step explanation:
For every 5 squares, two are red and three are green. So 3/5 of the squares are green.
3/5x55=33
The perpendicular distance of the point from x axis is 2 units and the perpendicular distance from y axis is 3 units.Write the co-ordinates of the if it lies in
Answer:
Step-by-step explanation:
Given that :
the perpendicular distance of the point from x axis = 2 units
the perpendicular distance from y axis is 3 units
The objective is to the write the coordinates of the points if it lies in
(i) | Quadrant (ii) || Quadrant (iii) ||| Quadrant (iv) |v Quadrant
The position of a point in a plane is conveniently specified by the distances fro two perpendicular lines.The lines are called the x-axis and y-axis and their [point of intersection is called the origin.
The perpendicular distance from the y-axis is called the x- coordinate or abscissa and the perpendicular distance from x-axis is called the y-coordinate or ordinate,The coordinate form an ordered pair with the abscissa written as first.
With that be said, So In the given question,
the perpendicular distance of the point from x axis = 2 units
y coordinate = ±2
the perpendicular distance from y axis is 3 units
x coordinate = ±3
The ordered pair of the coordinates = ( ±3, ±2)
Therefore;
in | quadrant ; we have (3,2) where x and y are both on the positive axis
in || quadrant ; we have (-3,2) x is on the negative axis and y is on the positive axis
In ||| quadrant ; we have (-3. -2) both x and y are on the negative axis
In |v quadrant ; we have ( 3, -2) x is on the positive axis and y is on the negative axis.
(10x²+19x+6) ÷(5x+2)
Answer:
2x + 3
Step-by-step explanation:
(10x² + 19x + 6) ÷ (5x + 2) =
= (10x² + 15x + 4x + 6) ÷ (5x + 2)
= [5x(2x + 3) + 2(2x + 3)] ÷ (5x + 2)
= [(5x + 2)(2x + 3)] ÷ (5x + 2)
= 2x + 3
Answer:
2x+3 is your answer
Graph the function f(x)=6x^5+8x^4-7x^3-5x^2+10 by making a table of values.
Answer:
Step-by-step explanation:
A fifth-grade polynomial requires a minimum of 6 different points to create an adequate graph. Let is [tex]X[/tex] the dominion of the polynomial, such that [tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]4[/tex], [tex]5[/tex] [tex]\in X[/tex]. The values of the function for each value are calculated herein:
x = 0
[tex]f(0) = 6\cdot 0^{5}+8\cdot 0^{4}-7\cdot 0^{3}-5\cdot 0^{2}+10[/tex]
[tex]f(0) = 10[/tex]
x = 1
[tex]f(1) = 6\cdot 1^{5}+8\cdot 1^{4}-7\cdot 1^{3}-5\cdot 1^{2}+10[/tex]
[tex]f(1) = 12[/tex]
x = 2
[tex]f(2) = 6\cdot 2^{5}+8\cdot 2^{4}-7\cdot 2^{3}-5\cdot 2^{2}+10[/tex]
[tex]f(2) = 254[/tex]
x = 3
[tex]f(3) = 6\cdot 3^{5}+8\cdot 3^{4}-7\cdot 3^{3}-5\cdot 3^{2}+10[/tex]
[tex]f(3) = 1882[/tex]
x = 4
[tex]f(4) = 6\cdot 4^{5}+8\cdot 4^{4}-7\cdot 4^{3}-5\cdot 4^{2}+10[/tex]
[tex]f(4) = 7674[/tex]
x = 5
[tex]f(5) = 6\cdot 5^{5}+8\cdot 5^{4}-7\cdot 5^{3}-5\cdot 5^{2}+10[/tex]
[tex]f(5) = 22760[/tex]
The table is now presented:
x y
0 10
1 12
2 254
3 1882
4 7674
5 22760
Finally, the graphic is now constructed by using an online tool (i.e. Desmos). The image is included below as attachment.
Evaluate the expression. Question 9 options: A) tan π∕56 B) tan 17π∕56 C) –tan 17π∕56 D) –tan π∕56
Answer:
A
Step-by-step explanation:
Note the expansion
tan(a - b) = [tex]\frac{tana-tanb}{1+tanatanb}[/tex]
We are given the right side of the expansion , then left side is
tan([tex]\frac{\pi }{7}[/tex] - [tex]\frac{\pi }{8}[/tex] )
= tan([tex]\frac{8\pi -7\pi }{56}[/tex] )
= tan ([tex]\frac{\pi }{56}[/tex] ) → A
A tap takes 3 hours to fill a tank. A discharge tap takes 6 hours to empty the same tank. How long will it take to fill the tank with both taps open?
Answer:
2 hours
Step-by-step explanation:
first tap= 3hours
therefore work done is = 1/3
second tap= 6hours
therefore work done = 1/6
so, 1/3+ 1/6
=2/6 + 1/6
=3/6
=1/2
=2/1 hours
=2 hours
root 6 x root 8 is equal to
Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
[tex]4\sqrt{3}[/tex] = [tex]\sqrt{6}[/tex] x [tex]\sqrt{8}[/tex]
Answer:
4 root 3 is the answer
Step-by-step explanation:
hope its help
solve for x 5(x+1)=4(x+8)
Answer:
x=27
Step-by-step explanation:
expanding the above expression we get
5x+5=4x+32
grouping numbers with coefficient of x at the left side and constant at the right side we get
5x-4x=32-5
x=27
46°
X
Х
X =
degrees.
Answer:
x = 67°
Step-by-step explanation:
The 2 base angles x are congruent , then
x = [tex]\frac{180-46}{2}[/tex] = [tex]\frac{134}{2}[/tex] = 67°
Answer:
X= 67 degrees.
Step-by-step explanation:
All triangles must add up to 180°. This is an isosceles triangle which means once you have one degree you can find the other two.
In order to get the answer start with 180°-46°
180-46=134
The two x's equal each other. So you can divide the remaining degrees by 2 to get the answer.
134÷2=67.
So the answer is 67°.
You and your friend want to find the proportion of yellow candies in a
candy machine. You take a sample of 30 candies. Your sample proportion
of yellow candies is 15%. Your friend takes 50 random samples of size 30
and her average proportion is 11%.
What is your estimate of the true proportion of yellow candies in the
machine? Why?
This question is solved using sampling, and proportions concepts.
The sample proportion is the point estimate for the population proportion, and we use this to find the estimate, which we find as 15% = 0.15, which is the sample proportion.
----------------------------------------------------
Proportion:
A proportion is the number of desired outcomes divided by the number of total outcomes.
----------------------------------------------------
In this question:
You take a sample of 30 candies. Your sample proportion
of yellow candies is 15%.
Thus, the point estimate of the true proportion of yellow candies in the sample, according to your sample, is of 15%.
----------------------------------------------------
A similar problem can be found at: https://brainly.com/question/24083999
Determine if the expression -5y^5-y^3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer:
Yes, it is a polynomial, and the degree is 5
Step-by-step explanation:
A polynomial is a combination of terms separated using + or − signs and normally have exponents. So, this equation is a polynomial. The degree is just the highest exponential value, which is 5 because -5y is being raised to the 5th power
PLEASE SOMEONE HELP ME WITH #2
AREA OF FIGURES. URGENT.
Answer:
big area/small area = (big length/small length)^2
24/small area = (6/3)^2
24/sa = 4
sa= 6
The vertex of the angle below is the center of the circle. Find n if n% of the circle is shaded. Give your answer as a mixed fraction.
Answer:
33 1/3 %
Step-by-step explanation:
120degree is shaded
There are 360 degrees in a circle
120/360
1/3
.33333
33 1/3 %
given m||n, find the value of x
Answer:
x = 127º
Step-by-step explanation:
y = 127º {Corresponding angles}
x = y {Vertically opposite angles}
x = 127º
Please help explanation if possible
Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....
Answer:Answer:
[tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]
Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as [tex]S_n = \frac{n}{2}[2a+(n-1)d][/tex]
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
[tex]S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70[/tex]
The sum of the nth term of the sequence will be;
[tex]S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)[/tex]
The sigma notation will be expressed as [tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]. The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.
Help me please. I need it
Answer/Step-by-step explanation:
Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], to solve each problem.
1. Distance between A(0, 0) and B(-5, 7):
[tex] (0, 0) = (x_1, y_1) [/tex]
[tex] (-5, 7) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(-5 - 0)^2 + (7 - 0)^2} = \sqrt{(-5)^2 + (7)^2} = \sqrt{25 + 49} [/tex]
[tex] AB = \sqrt{74} [/tex]
2. Distance between A(-3, 1) and B(-11, 1):
[tex] (-3, 1) = (x_1, y_1) [/tex]
[tex] (-11, 1) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(-11 - (-3))^2 + (1 - 1)^2} = \sqrt{(-8)^2 + (0)^2} = \sqrt{64 + 0} [/tex]
[tex] AB = \sqrt{64} = 8 [/tex]
3. Distance between A(-3, -2) and B(5, 6):
[tex] (-3, -2) = (x_1, y_1) [/tex]
[tex] (5, 6) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(5 - (-3))^2 + (6 - (-2))^2} = \sqrt{(8)^2 + (8)^2} = \sqrt{64 + 64} [/tex]
[tex] AB = \sqrt{128} = \sqrt{64*2} [/tex]
[tex] AB = 8\sqrt{2} [/tex]
4. Distance between A(-2, -5) and B(-6, 1):
[tex] (-2, -5) = (x_1, y_1) [/tex]
[tex] (-6, 1) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(-6 - (-2))^2 + (1 - (-5))^2} = \sqrt{(-4)^2 + (6)^2} = \sqrt{16 + 36} [/tex]
[tex] AB = \sqrt{52} [/tex]
None of the choices are correct
In which direction must the graph of Ax) = x be shifted to produce the graph of g(x) = f(x) - 4?
ОА. up
OB. down
O c. left and down
OD. right and up
Answer: B. down
Step-by-step explanation:
Translation rules:
For a function h(x):
h(x+c) is a left-shift by c units.h(x-c) is a right-shift by c units.h(x)+c is a up-shift by c units.h(x)-c is a down-shift by c units.Here, the graph of f(x) becomes the graph of g(x) =f(x)-4 which is similar to "h(x)-c".
That means , f(x) is shifted 4 units down to become g(x).
So, correct option : B. down
A baking scale measures mass to the tenth of a gram up to 650 grams .Which of the following measurements is possible
Answer:
A. 3.8 grams
Step-by-step explanation:
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale?
a.3.8 grams
b.120.01 grams
c.800.0 grams
d.54 milligrams
Solution
The scale measures mass to the tenth of a gram
The scale measures up to 650 grams
a.3.8 grams
This measures to the tenth of a gram (to one decimal place) and it is not up to 650 grams
b.120.01 grams
This measures to hundredth of a gram ( 2 decimal places) and it is not up 650 grams.
c.800.0 grams
This measures to the tenth of a gram but exceeds the 650 grams limit
d.54 milligrams
This is in milligram, so it is wrong
Option a.3.8 grams is the only possible scale measurement among the options.
10.
J
A
B
0
L
с
K
Not drawn to scale
JK, KL, and are all tangent to circle O. JA = 9, AL = 10, and CK = 14. What is the perimeter of AJKL?
66 units
46 units
O 33 units
38 units
Answer:
66
Step-by-step explanation:
The figure of triangle JKL is attached. JA = 9, AL = 10, and CK = 14.
According to two tangent theorem, the tangent to a circle that meets at the same point is equal to each other. Therefore:
AJ = BJ, AL = CL, CK = BK.
Since AJ = 9, BJ = AJ = 9
AL = 10, CL = AL = 10
CK = 14, BK = CK = 14.
Therefore the lengths of the triangle sides are:
JL = AJ + AL = 9 + 10 = 19
JK = BJ + BK = 9 + 14 = 23
KL = CL + CK = 14 + 10 = 24
The perimeter of the triangle is the sum of all its sides, it is given as:
Perimeter = JL + JK + KL = 19 + 23 + 24 = 66
factories each of the following −2x2 −20x −18
Answer:
2(x + 9)(x + 1)
Step-by-step explanation:
First, take out a GCF if possible. Each coefficient is dividable by 2, so 2 is the GCF.-2(x^2 + 10x + 9)
→ The main quadratic equation is equal to ax^2 + bx + c.
Then, use a factoring pattern to factor the expression in parentheses. The factors of C that add up to equal B are the two factors.2(x + 9)(x + 1)
The expression cannot be factored any further.
If m ZABD = 78°, what are mZABC and mZDBC?
(5x+3)
(5x-5)
Hi, I'm happy to help!
First, we need to solve for x. We know that ABD is 78 degrees. (5x+3), and (5x-5) combined are also 78 degrees. So, we combine the like terms of these to get a new expression.
(5x+3) +(5x-5)
10x-2=78
From here, we want to single out the x, by editing both sides in the same way.
10x-2=78
+2 +2
10x=80
÷10 ÷10
x=8
Now that we know what x is, we can plug it in to the previous expressions to get the angles of ABC and DBC.
(5x-5)
((5·8)-5)
(40-5)
35
Now, we know that ABC is 35 degrees.
(5x+3)
((5·8)+3)
(40+3)
43
Now, we also know that DBC is 43 degrees.
To verify our answer we can add ABC and DBC together to check if it totals to ABD.
35+43=78
Now, we know that the answer: ABC is 35 degrees and DBC is 43 degrees is correct.
I hope this was helpful, keep learning! :D
If x =2.3,5x.3= DONT MAKE ANSWERS THAT DONT MAKE ANY SENSE OR YOU WILL GET REPORTED
Answer:
34.5
Step-by-step explanation:
5 times x(2.3) = 11.5.
11.5 times 3 is 34.5
you put 2.3 in place of x because x was the unknown value, but now that we know it is 2.33 we plug it in.
An inchworm (exactly one inch long, of course) is crawling up a yardstick (guess how long that is?). After the rst day, the inchworm's head (let's just assume that's at the front) is at the 3" mark. After the second day, the inchworm's head is at the 6" mark. After the third day, the inchworm's head is at the 9" mark. Let d equal the number of days the worm has been crawling. (So after the rst day, d = 1.) Let h be the number of inches the head has gone. Let t be the position of the worm's tail.
A model of a wedge of cheese is used in a display for a deli. All the sides of the model are covered in yellow construction paper. A rectangular prism has a rectangular base with length of 15 centimeters and height of 5 centimeters. Another rectangle has length of 15 centimeters and height of 13 centimeters. Another rectangle has length of 15 centimeters, and height of 12 centimeters. The triangular sides have a base of 5 centimeters and heights of 12 centimeters. How much construction paper is needed for the model? 45 square cm 330 square cm 510 square cm 570 square cm
Answer:
510 cm²
Step-by-step explanation:
To find how much construction paper is needed for the model, we calculate the total areas of each of its sides.
The area of the first triangular sides is A₁ = 15 cm × 5 cm = 75 cm²
The area of the second triangular sides is A₂ = 15 cm × 13 cm = 195 cm²
The area of the third triangular sides is A₃ = 15 cm × 12 cm = 180 cm²
The area of each triangular side is A₄ = 1/2 × 5 cm × 12 cm = 30 cm²
The area of the two triangular sides is A₅ = 2A₄ = 2 × 30 cm² = 60 cm²
The total surface area of a wedge of cheese is A = A₁ + A₂ + A₃ + A₅ = 75 cm² + 195 cm² + 180 cm² + 60 cm² = 510 cm²
So the amount of construction paper needed equals the total surface area of the wedge of cheese = 510 cm²
Answer:
510
Step-by-step explanation:
Number of minutes 1 2 3 4 5 6 7 8 9 10
Number of trainees 2 3 5 10 15 30 25 15 10 5
1.) use the data to draw a bar chart
Answer: please find the attached file for the graph.
Step-by-step explanation:
Number of minutes 1 2 3 4 5 6 7 8 9 10Number of trainees 2 3 5 10 15 30 25 15 10 5
Given that data set above, the time in minutes will be on the x axis while the number of trainees will be in the y axis.
In bar chart, the bars will not touch each other.
Please find the attached file for the solution and figure
4x
5.
If 7:5 = (x + 2y): (x - y), find the value of
5y
Answer:
5/2 OR 2.5
Step-by-step explanation:
( x + 2y ) = 7 , ( x - 2y ) = 5
x = 7 - 2y , x = 5 + 2y
substitute the two eqns together:
7 - 2y = 5 + 2y
7 - 5 = 2y + 2y
2 = 4y
y = 1/2
when y = 1/2 ,
5y = 5(1/2)
= 5/2 OR 2.5
What is the coefficient of the variable in the expression 6 − 4x − 8 + 2
Answer:
-4
Step-by-step explanation:
6 − 4x − 8 + 2
The variable is x
The coefficient is the number in front of the variable ( it will include the sign)
-4 is the coefficient
Answer:
-4
Step-by-step explanation: