nick bought a pet lizard and enjoys the responsibility of taking care of it . every week , the lizard will eat 60 grasshoppers. nick pays $1 for 20 grasshoppers . how many dollars will a year’s worth of food cost for the lizard
60*52 = 3120 per year
3120/20 = 156
it will cost $156 a year
Write an expression that is equivalent to 2/3 (4x + 9).
8/3x + 6
8/3x + 9
2/3x + 6
2/3x + 9
2/3 of 9 = 6
2/3 *4 = 8/3
so the answer would be 8/3x +6
What is the angle of elevation from jim to the top of the waterfall
Answer: <7
Step-by-step explanation:
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The angle of elevation from Jim to the top of the waterfall is ∠5. The correct option is B.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The angle of elevation is an imaginary angle that is assumed between the horizontal line and the line through which an object at a height is been seen.
In the given image the angle of elevation from Jim to the top of the waterfall is the angle formed by the line parallel to the horizontal plane and the line that connects Jim's eyesight to the top of the waterfall.
Hence, the angle of elevation from Jim to the top of the waterfall is ∠5.
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Which expression is equivalent to -3.5(4x – 3)?
A. -3.9x – 3.2
B. -3.9x + 3.2
C. -14x + 10.5
D. -14x – 10.5
Answer:
The answer is c
Step-by-step explanation:
Complete the pairs of 's.
(triangle)FCA ~= (triangle)
DAC
EBC
GCA
Answer:
DAC
Step-by-step explanation:
We can write, from the figure of the question.
In ΔFCA and ΔDAC.
∠FAC=∠DCA,
AC=CA, (common)
∠FCA=∠DAC.
Hence , we can say ΔFCA ≅ ΔDAC, because here in ΔFCA and ΔDAC, the two corresponding angles and including side are same (from ASA postulate ).
If a share of stock costs $32.63, what would it cost to buy 1,000 shares of the stock?
What is the ratio 35 to 15 expressed as a fraction in simplest form?
how would you graph the solution set of the system of inequalities {3y≤2x+6} { 2x+y>0}
what is the least common factor of 54 and 77
Two angles are complementary. the measure of one angle is 21 more than the measure of the other angle. find the measures of the angles
4. The science team uses the information to suggest the main outcome of the hypothesis.
a. Make a prediction
b. Test the hypothesis
c. observe the problem
d. Define a problem
5. This step includes recording data, taking photos, and coordinating information.
a. Make a prediction
b. Test the hypothesis
c. observe the problem
d. Define a problem
You spend 5/6 of the money in your pocket on new clothes for school. The amount you spend on jeans for school is 2/5 of the total amount you spend on all your school clothes.
What fraction of the original amount of money in your pocket do you spend on jeans?
Can someone help me with this? 18(−8c+16)−13(6+3c) =
Find the length of the diagonal of this rectangle.
Answer:
The length of the diagonal of the given Rectangle is, 11.80 m (Approx.)
Step-by-step explanation:
In Rectangle:
* It is a four sided shape where every angle is a right angle.
* The alternative sides are equal.
*Two axes of symmetry bisect each other.
* Diagonals are equal in length.
The figure of rectangle has given the length [tex]l[/tex] = 10m
In right angle triangle ADC.
DC = 10 m ( as alternative sides are equal )
Note that we are given here the adjacent and we have to find the length of hypotenuse, then we use trigonometric ratio that contains both sides adjacent and hypotenuse.
Use: [tex]Cosine = \frac{Adjacent}{hypotenuse}[/tex]
then,
[tex]\cos 32^{\circ} = \frac{10}{AC}[/tex] or
[tex]Ac = \frac{10}{\cos 32^{\circ}} =\frac{10}{0.8480481}[/tex]
On simplify we get;
AC = 11.791784 m
therefore, the length of the diagonal of this rectangle (AC) is, 11.80 m (Approx)
Consider the function
{8x-x^2 for x is less than or equal to 8
x^2+3 for x>8}
what is f(8)?
Help please !!!!!!!!!!!!!!
The legs of a right triangle measure 30cm and 40cm.what is the length of the hypotenuse
if i have 64,32,16,8 what two numbers comes next
A company plans to enclose three parallel rectangular areas for sorting returned goods. the three areas are within one large rectangular area and 10641064 yd of fencing is available. what is the largest total area that can be enclosed?
First get the perimeter
Perimeter: 2l + 2w = 1064 yd
The region inside the fence is the area
Area: A = lw
We need to solve the perimeter formula for either length or width.
2l + 2w = 1064 yd
2w = 1064 yd – 2l
W = 1064– 2l / 2
W = 532 – l
Now substitute than to the area formula
A = lw
A = l (532 – l)
A = 532 – l^2
Since the equation A represents a quadratic expression, rewritte the expression with the exponents in descending order
A(l) = -l^2 + 532l
Then look for the value of the x coordinate
l = -b/2a
l = -532/2(-1)
l = -532/-2
l = 266 yards
Plugging in the value into our calculation for area:
A(l) = -l^2 + 532
A(266) = -(266)^2 + 532 (266)
A(266) = 70756+ 141512
= 70756 square yards.
Thus the largest area that could encompass would be a square where each side has a length of 266 yards and a width of:
W = 532 – l
= 532 – 266
= 266
It should be noted that the largest total area that can be enclosed will be 70756 yards².
How to calculate the area.Firstly, we have to calculate the perimeter. This will be:
2l + 2w = 1064 yd
Area: A = length × width
2l + 2w = 1064 yd
2w = 1064 yd – 2l
W = 1064– 2l / 2
W = 532 – l
Since Area = lw
A = l(532 – l)
A = 532 – l²
A(l) = -l² + 532l
l = -b/2a
l = -532/2(-1)
l = -532/-2
l = 266 yards
The length is 266 yards.
Area = -l² + 532
A( = -(266)² + 532 (266)
Area = 70756+ 141512
Area = 70756 yards²
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What? I don’t know what I’m doing???
a rectangle has a diagonal which is 4 times the width if the area is 15root2 what are width andperimeter of the rectangle
What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ?
Enter your answer in the box.
we know that
A method for calculating the area of a triangle when you know the lengths of all three sides is the Heron's Formula.
The Heron's Formula states that
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
a,b.c are the length sides of the triangle
p is half the perimeter of the triangle
Let
[tex]A(-4,1)\\B(-7,5)\\C(0,1)[/tex]
Step 1
Find the distance AB
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,1)\\B(-7,5)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(5-1)^{2}+(-7+4)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]dAB=5\ units[/tex]
Step 2
Find the distance BC
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]B(-7,5)\\C(0,1)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(1-5)^{2}+(0+7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(7)^{2}}[/tex]
[tex]d=\sqrt{65}[/tex]
[tex]dBC=8.06\ units[/tex]
Step 3
Find the distance AC
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,1)\\C(0,1)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(1-1)^{2}+(0+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]d=\sqrt{16}[/tex]
[tex]dAC=4\ units[/tex]
Step 4
Find half the perimeter
[tex]p=\frac{1}{2}(AB+BC+AC)[/tex]
substitute the values
[tex]p=\frac{1}{2}(5+8.06+4)[/tex]
[tex]p=8.53\ units[/tex]
Step 5
Find the area
Applying the Heron's Formula
[tex]A=\sqrt{8.53(8.53-5)(8.53-8.06)(8.53-4)}[/tex]
[tex]A=\sqrt{8.53(3.53)(0.47)(4.53)}[/tex]
[tex]A=\sqrt{64.11}[/tex]
[tex]A=8\ units^{2}[/tex]
therefore
the answer is
the area of the triangle is [tex]8\ units^{2}[/tex]
The area of a shape is the amount of space it occupies.
The area of the triangle is 8 unit square.
The vertices are given as:
[tex]\mathbf{A = (-4,1)}[/tex]
[tex]\mathbf{B = (-7,5)}[/tex]
[tex]\mathbf{C = (0,1)}[/tex]
The area of the triangle is:
[tex]\mathbf{A= \frac{1}{2} \times |A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}[/tex]
So, we have:
[tex]\mathbf{A= \frac{1}{2} \times |-4(5 - 1) -7(1 - 1) + 0(1 - 5)|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -7(0) + 0|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -0 + 0|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-16|}[/tex]
Remove absolute brackets
[tex]\mathbf{A= \frac{1}{2} \times 16}[/tex]
[tex]\mathbf{A= 8}[/tex]
Hence, the area of the triangle is 8 unit square.
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Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $27 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has no monthly fee but charges $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
What is the y-intercept of the line? y +6x - 4y-intercept =?
Answer:
[tex]\huge\boxed{\boxed{\tt{the \ y-intercept \ is \ -4}}}[/tex]
Step-by-step explanation:
Hello.
The equation is written in slope-intercept form (y-mx+b, where m stands for the slope of the line and b stands for the y-intercept)
Let's write the equation and see if we can identify its y-intercept (the point where the graph touches the y-axis)
Equation:
[tex]{\boxed{\boxed{\bf{y=6x-4}}}[/tex]
Y-intercept:
[tex]\boxed{\boxed{-4}}[/tex]
And we're done!
Note: The slope of the line is 6.
I hope it helps & have an outstanding day!
~ST2710
Pythagorean Theorem. I need help please!!!!!
The Scott Shop charges $27 more than the Garcia Co. for a winter jacket. If the Scott shop’s price is $77, how much does the Garcia Co. charge?
subract 27 from 77
77 -27 =50
Garcia charges 50 dollars
The floor of a shed has an area of 99 square feet. the floor is in the shape of a rectangle whose length is 7 feet less than twice the width. find the length and the width of the floor of the shed. use the formula, area equals=length times•width.
Final answer:
The width is 9 feet and the length is 11 feet.
Explanation:
The area of a shed floor is given as 99 square feet, and the floor is shaped like a rectangle. According to the problem, the length (L) of the floor is 7 feet less than twice the width (W). The relationship between length and width can be expressed as L = 2W - 7. We can use the area formula, which is Area = Length × Width.
Given the area (A) is 99 sq ft, we can set up the equation:
A = L × W
99 = (2W - 7) × W
Now we solve for W using the quadratic equation:
W2 - 7W + 99 = 0
Upon solving, we find that W = 9 feet (since the width cannot be negative). Now we can find the length L by substituting W into the length expression:
L = 2 × 9 - 7 = 11 feet
Therefore, the width is 9 feet and the length is 11 feet.
write a word phrase for each algebraic expression
1. 25 - 6
2. 2/3y + 4
factor each expression
3. 45c + 10d
4. 27 - 9x + 15y
Simplify the expression.
5. 3(t - 4) - 8 (2 - 3t )
6. 12x + 24
Answer:
Step-by-step explanation:
1)Twenty five minus sixty percent times a number.
A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 780-meter head start. When the start gun is fired the hare begins running at a constant speed of 10 meters per second and the tortoise begins crawling at a constant speed of 5.3 meters per second.
Can you find a shortcut in doing two translations in geometry