Considering a width x of the sand path, we have a larger rectangle of dimensions 50+2x by 34+2x, as indicated in the figure. Now, the area of the sand path is expressed.
[tex]\boldsymbol{\sf{ (50+2x)(34+2x)-50\times 34=540\Longrightarrow\quad 0=4x^2+168x-540 }}[/tex]
[tex]\boldsymbol{\sf{ 0=4(x^2+42x-135)=4(x-3)(x+45) }}[/tex]
Therefore, the path is 3 m long.
help me help The function h is defined by the following rule.
Answer:
-1
-2
-5
-4
-1
Step-by-step explanation:
plug in each given number for x in the function:
- (-4) - 5
a negative negative is also a positive
4 - 5 = -1
- (-3) - 5
3 - 5 = -2
0 - 5 = -5
1 - 5 = -4
4 - 5 = -1
Help please I’ll give 75 brainly credits
Answer:
213 inches^2
Step-by-step explanation:
the ^2 is the exponent
Surface Area = 2×(6×9 + 6×3.5 + 9×3.5)
Please mark brainliest
Answer:
So we are given the length, width, and height and we are also told that we need to find the surface area. The formula to finding the surface area of a rectangular prism is [tex]S=2(w*h+l*w+l*h)[/tex]
We just plug in the values and solve
[tex]S = 2(9\ in * 3.5\ in+6\ in * 9\ in + 6\ in * 3.5\ in)[/tex]
[tex]S = 2(31.5\ in^2 + 54\ in^2+21\ in^2)[/tex]
[tex]S = 2(106.5\ in^2)[/tex]
[tex]S = 213\ in^2[/tex]
Hope this helps! Let me know if you have any questions
Each dot on the dot plot shows the number of people in a 12-person random sample who are shorter than 5 feet tall.
A dot plot with 2 dots above 1; 4 dots above 2; 4 dots above 3; 3 dots above 4; 1 dot above 5; and 1 dot above 10.
How many samples does the dot plot represent?
Enter your answer as a number, like this: 42
Answer:
15
Step-by-step explanation:
sucks to suck
Triangle JKL has vertices J(−3, 1), K(0, 3) and L(4, −2). What are the coordinates of vertex L after the triangle is translated 2 units right and and 5 units down?
Answer:
L translated is now (6, -7)
Tara just bought her first car in order to commute to college, a used 2014 Toyota RAV4! The value of the car today is $13,000, but will lose 11% of it’s value each year for the next several years. Down the road, Tara will trade the RAV4 in for a down payment on a newer car. If she trades in her car 4 years from now, how much will it be worth?
The future value after 4 years will be $8156.49 if the value of the car today is $13,000 but will lose 11% of its value each year for the next several years.
What is future value?Based on an estimated growth rate, the future value is the amount that an asset will be valued at a future date. The computation assumes that at the start date, a fixed amount of cash is made available for investment and that it increases at a constant rate until the selected future date.
We have:
Current value of the car = $13,000
Depreciation rate = 11%
Time n = 4 years
[tex]\rm Future \ value = (value \ at \ present) ( 1- \dfrac{depreciation \ rate}{100})^n[/tex]
[tex]\rm Future \ value = (13000)(1-\frac{11}{100} )^4[/tex]
Future value = $8156.49
Thus, the future value after 4 years will be $8156.49 if the value of the car today is $13,000 but will lose 11% of its value each year for the next several years.
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16. Prove that the sum of three angles of triangle is two right angles.
Answer:
Two right angles = 180 degrees
Step-by-step explanation:
A right angle = 90 degrees
The sum of the interior angles of a triangle = 180 degrees
Two right angles (2 * 90) = 180
180 = 180
Therefore, the sum of the interior angles of any triangle is equal to two right angles.
PLEASE HELP!!!!!!!!!!!!!!!!!
Answer:
<
Step-by-step explanation:
note that
| - y | = y
and
- | y | = - y
then
- y < y
In the parallelogram above, if angle R is 56 degrees, what is the value of x + y?
Answer:
248
Step-by-step explanation:
Consecutive angles of a parallelogram are supplementary.
56 + y = 180
y = 180-56
y =124
The opposite angles of a parallelogram are equal.
x = y = 124
x+y = 124+124
=248
Answer:
x + y = 248
Step-by-step explanation:
consecutive angles in a parallelogram sum to 180°
opposite angles are congruent
x + 56° = 180° ( subtract 56° from both sides )
x = 124°
then
y = x = 124 , so
x + y = 124 + 124 = 248
The length of a rectangle is 7 more than the width. The area is 744 sqaure yards, find the length and width of the rectangle
Answer:
Length of rectangle is 31 yards and Width is 24 yards.
Given:
The length of a rectangle is 7 more than the width. The area is 744 sqaure yardsSolution:
Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.
Using formula
[tex] \\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\ [/tex]
On Substituting the required values, we get;
[tex]\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\ [/tex]
As we know that width of the rectangle can't be negative. So x = 24
Hence,
Width of rectangle = x = 24 yardsLength of the rectangle = x + 7 = 31 yards[tex] \therefore[/tex]Length of rectangle is 31 yards and Width is 24 yards.
Avery solves the equation below by first squaring both sides of the equation.
Answer:
z = 7/3 is extraneous.
Step-by-step explanation:
√(z^2+8) = 1 - 2z
z^2 + 8 = (1 - 2z)^2
z^2 + 8 = 1 -4z + 4z^2
3z^2 - 4z - 7 = 0
3z^2 + 3z - 7z - 7 = 0
3z(z + 1) - 7(z + 1) = 0
(3z - 7)(z + 1) = 0
3z = 7, z = -1
z = 7/3, -1.
One of these might be extraneous.
Checking:
√(z^2+8) = 1 - 2z, if z = -1:
√(1 + 8) = 3, -3
1 - 2(-1) = 3. So its not z = -1
if z = 7/3
√((7/3)^2 + 8) = 13.44
1 - 2(7/3) = -3.66
So its z = 7/3
Answer:
[tex]z=\dfrac{7}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{z^2+8}=1-2z[/tex]
Square both sides:
[tex]\implies (\sqrt{z^2+8})^2=(1-2z)^2[/tex]
[tex]\implies z^2+8=1-4z+4z^2[/tex]
Subtract [tex]z^2[/tex] from both sides:
[tex]\implies 8=1-4z+3z^2[/tex]
Subtract 8 from both sides:
[tex]\implies 0=-7-4z+3z^2[/tex]
[tex]\implies 3z^2-4z-7=0[/tex]
Rewrite the middle term:
[tex]\implies 3z^2+3z-7z-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 3z(z+1)-7(z+1)=0[/tex]
Factor out the common term [tex](z+1)[/tex]:
[tex]\implies (3z-7)(z+1)=0[/tex]
Therefore:
[tex]\implies (z+1)=0 \implies z=-1[/tex]
[tex]\implies (3z-7)=0 \implies z=\dfrac{7}{3}[/tex]
To find the extraneous solution (the root that is not a root of the original equation), enter the two found values of z into the original equation:
[tex]\begin{aligned}z=-1\implies \sqrt{(-1)^2+8}&=1-2(-1)\\\implies 3&=3\implies \textsf{true}\\\end{aligned}[/tex]
[tex]\begin{aligned}z=\dfrac{7}{3} \implies \sqrt{\left(\frac{7}{3}\right)^2+8}&=1-2\left(\frac{7}{3}\right)\\\implies \dfrac{11}{3} &=-\dfrac{11}{3}\implies \textsf{false}\end{aligned}[/tex]
[tex]\textsf{As}\: \dfrac{11}{3} \neq -\dfrac{11}{3}\:\textsf{then}\: z=\dfrac{7}{3}\:\textsf{is the extraneous solution}[/tex]
Which statement is true?
All squares are rhombuses. Rhombuses have 4 right angles. Therefore, all squares have 4 right angles.
Only some squares are rhombuses. Rhombuses have 4 sides that are the same length. Therefore, only some squares have 4 sides that are the same length.
All squares are rhombuses. Rhombuses have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.
Only some squares are rhombuses. Rhombuses have 4 right angles. Therefore, only some squares have 4 right angles.
Answer:
C) All squares are rhombuses. Rhombeses have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.
Step-by-step explanation:
Rina Botwright receives $624 gross salary biweekly. Her income tax rate is 14%. Her group health plan contribution is $4.25 per pay period. She belongs to the company retirement plan, to which she contributes 6% of her earnings. She is also covered under Social Security benefits. Her current contribution is 6.05%
If these items are all her deductions, what is her take-home pay per period?
Rina gets a $35 raise per pay period. If her health plan is unchanged, how much of the raise will she have to take home?
take-home pay per period = $
amount of raise taken home = $
Rina Take home pay is $457.20
what is Salary percentage?
The basic salary divided by the Gross salary is multiplied by 100. The result is the percentage of gross salary.
Given that:
gross salary = $624
14% income tax = 624* 0.14 = $87.36
group health plan = $4.25
Company retirement = 624 * 0.060 =$37.44
Social Security = 624 * 0.0605 = $37.752
Home pay= 624 - 87.36 - 4.25 - 37.44- 37.752
= 457.198
Her take home pay is $457.198
if she gets a $35 raise per pay period,
So, new gross salary would be,
= $624 + $35
= $659.
Again, we have
14% Income tax = 659 * 0.14 = $92.26
Group health plan = $4.25
Company retirement = 659 * 0.060 = $39.54
Social Security = 695* 0.0605 = $39.8695
Home take pay,
=659-39.8695 - 45.825 - 39.54-92.26
=441.5055
Her take home pay is $441.5055
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Help pls with give brainilist
Can someone please help
Answer:
7.62
Step-by-step explanation:
3 x 3 = 9, 7 x 7 = 49, 49 + 7 = 58. Square root of 58 = 7.62
Answer:
hypotenuse ≈ 7.6 units
Step-by-step explanation:
calculate the length using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1} )^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, - 3) and (x₂, y₂ ) = (2, 4) ← endpoints of hypotenuse
d = [tex]\sqrt{(2-(-1))^2+(4-(-3))^2}[/tex]
= [tex]\sqrt{(2+1)^2+(4+3)^2}[/tex]
= [tex]\sqrt{3^2+7^2}[/tex]
= [tex]\sqrt{9+49}[/tex]
= [tex]\sqrt{58}[/tex]
≈ 7.6 ( to the nearest tenth )
please help me asap help help please please help me please please
Answer:
d.45 sq.ft
Step-by-step explanation:
Surface are i.e. Total surface area of square pyramid = a^2 + 2al
where a^2 is area of base
a is side of base
l is slant height
by the figure
a=3ft
a^2 = a×a
=3×3
=9ft
l=6ft
Surface area = a^2+2al
=9+2×3×6
=9+36
=45 sq.ft
what is value of 3(√3(80-x)
Answer:
= 240√3-3√3x
Step-by-step explanation:
parentheses:
=3√3 (80 – x)
Apply the distributive law:
a=3√3, b= 80, c =X
=3√3×80-3√3x
=3× 80√3 -3√3x
Multiply the numbers: 3×80 = 240
= 240√3-3√3x
Solve for m < L
Enter your answer in the box. Round your final answer to the nearest degree.
The cosine is the ratio of hypotenuse and base. Then the measure of the angle ∠L will be 60°.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The right-angle triangle is given below.
The length of the hypotenuse is 16 and the base length is 5.
Then the measure of the angle ∠L will be
cos L = 5 / 10
cos L = 1 / 2
L = cos⁻¹ (1 / 2)
L = 60°
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solve the inequality -28n is less than or equal to 7
Answer:
n >= -1/4
Step-by-step explanation:
Divide both sides by the same factor, and flip the relation because the factor is negative
-28n/-28 >= 7/-28
Simplify,
Cancel terms that are in both the numerator and denominator.
n >= 7/-28
Divide the numbers.
n >= 7/-28 = n >= -1/4
The answer is n >= -1/4
Hope this helps!
Which is the explicit rule for the geometric sequence? 10,-30,90,-270,…
an=-1/3n+10
an=10(-3)n-1
an=-10(1/3)n-1
an=-3n
Answer:
the ans is c
Step-by-step explanation:ive done it b4
The density of an unknown piece of metal is 20g/mL, if the mass of the metal is 40g, what is the volume of the unknown metal?
Answer:
Density = mass / volume
thus, volume = mass / density
volume = 40 / 20 = 20 mL
Claire has $88.50 in her bank account. She gets paid for 8 hours of work and deposits her entire paycheck. Now she has $180.50 in her account. How much does Claire earn per hour?
Michelle started doing a puzzle at 7:50 p.m. She finished the puzzle at 8:34 p.m. How long did Michelle work on the puzzle?
Answer:
44 minutes
Step-by-step explanation:
Given:
Michelle started doing a puzzle at 7:50 p.m. She finished the puzzle at 8:34 p.m.
To Find:
How long did Michelle work on the puzzle?
Solve:
Began Time ⇒ 7:50 p.m
End Time ⇒ 8: 34 p.m
Since they are both p.m we could just subtract 8:34 by 7:50.
But first we know that:
8: 34 the 34 can't be subtracted by 7:50 the 50.
Thus we know that:
1 Hour = 60 minutes
Hence,
changing 8:34 p.m from 1 hour to 60 minutes. Which given us 7:94.
Then,
7:94 - 7:50
= 44
Hence, Michelle work on the puzzle for 44 minutes.
Kavinsky
Help me please 50 points and brainliest.
The answer is -2
Sure hope this helps you
Help me!!!!
I don’t understand the equation
Step-by-step explanation:
it does not matter, if you understand the equation itself. look at the graph ! what is the curve doing ?
I don't know the options of the pull-down menus, so I will give you my best guesses based on the facts :
the domain of a function is the set or interval of all valid x (or input) values.
the range of a function is the set of interval of all valid y (or functional result) values.
so, clearly, x is in the interval (-infinity, +infinity). which is therefore the domain.
please conduct the round brackets. they indicate that the specified interval limits are not included (as infinity is not a value, only a concept, and can never be reached).
and y is in the interval of (0, +infinity). which is therefore the range.
we have to use the round brackets also for 0, as the function will never deliver the value 0, but its tendency or limit goes there (but again, only in infinity, which will never be reached).
the function continuously decreases when x increases.
again, I am not sure what the options are here, and what your teacher wants to "hear".
At an assembly, 7 out of the first 12 students who entered the gym were carrying a backpack. Based on this information, if 648 students were at the assembly, how many students could be expected to be carrying a backpack?
The number of students that are expected to carry a backpack is = 378
Calculation of total number of studentsThe total number of students in the assembly= 648
The number of students that enters the gym =12
The number of students carrying backpack = 7 out of 12
The total number of batches that entered the gym = 648/12 = 54
Therefore, the number of students that are expected to carry a backpack is = 54 ×7 = 378
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An observer (O) spots a bird flying at a 35° angle from a line drawn horizontal to its nest. If the distance from the observer (O) to the bird (B) is 21,000 feet, how far is the bird (B) from its nest (N)? Round to the nearest whole number. A right triangle BNO is shown with angle B marked 35 degrees, side BN marked x, and side BO marked 21,000 feet.
the answer is 17,202 feet
The bird (B) from its nest (N) is 17202 ft.
What is Trigonometric functions?
Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
This is very obviously a right triangle problem.
Side BO is the hypotenuse of the triangle, measuring 21000.
Side BN is the side adjacent to the given angle B, 35 degrees.
This is the cosine ratio:
cos∅ = adj/hyp
substitute the values
cos35° = x/21000 and solving for x:
21000.cos(35°) = x
x = 17202.19 or, rounded as we need:
x = 17202
Hence, the bird (B) from its nest (N) is 17202 ft
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Can someone please answer this, ill give you brainliest Would be very appreciated.
For the function: y = x² + 4
y intercept: (0, 4)x intercept: Nonevertex: (0, 4)For the function: x² - 4
y intercept: (0, -4)x intercept: (-2, 0) and (2, 0)vertex: (0, -4)For the function: 1 - x²
y intercept: 1x intercept: (1, 0) and (-1, 0)vertex: (0, 1)Conclusion:
green line = x² + 4; blue line = x² - 4; black line = 1 -x²
Answer:
See below ~
Step-by-step explanation:
Equation of Graph A :
No x-interceptsY-intercept at (0, 4)y = x² + 4Equation of Graph B :
x-intercepts at (-2, 0) and (2, 0)y = (x - 2)(x + 2)y = x² - 4Equation of Graph C :
opens downwards ⇒ coefficient of x² is -vex-intercepts at (-1, 0) and (1, 0)y = - (x + 1)(x - 1)y = -x² + 1y = 1 - x²help please and show work<3!
The figure shown in the question is a rectangle because it has four sides and two opposite sides are parallel.
What is the rectangle?A rectangle is a quadrilateral having four sides the two opposite sides of the rectangle are equal and parallel. and the two sides are always at perpendicular to each other.
here in the figure we have four sides and two opposite sides are equal
and also parallel to each other so the given figure is the triangle.
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Mateo is roasting a chicken. He must make sure the chicken has a minimum internal temperature of 165 degrees so that it is
safe to eat. Using a thermometer, he takes the temperature of the chicken in three random places. The minimum temperature in
the sample is 172 degrees.
Identify the population and the sample. (4 points)
• Population: 165 degrees; Sample: 172 degrees
• Population: 172 degrees; Sample: 165 degrees
• Population: all the chicken meat; Sample: 172 degrees
• Population: three random places in the chicken; Sample: all the chicken meat
• Population: all the chicken meat; Sample: three random places in the chicken
Using sampling concepts, it is found that the population and the sample are given by:
Population: all the chicken meat; Sample: three random places in the chicken.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population.
In this problem, a group of 3 chicken meat is taken from all the chicken meat, which is the population, hence the correct option is given by:
Population: all the chicken meat; Sample: three random places in the chicken.
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X^5/6 / x^1/6 radical form
Answer:
x ^ 4
Step-by-step explanation:
X x 5/6 / X x 1 / 6 = 5/6 - 1/6 = 4
then it = X^4
