Answer:
t= $ 6.75 cost for table
c= $ 1.50 chair cost
Step-by-step explanation:
Answer:
chair 2.50
table 8.50
Step-by-step explanation:
Find the product 12, -5
12• (-5)= - 120/2 = -60
ANSWER
The product is
[tex] - 60[/tex]
EXPLANATION
We want to find the product of 12 and -5.
This means that we should find the result of multiplying 12 and -5
Recall that:
[tex]12 \times 5 = 5 \times 12 = 60[/tex]
Therefore,
[tex]12 \times ( - 5) = - 5 \times 12 = 60[/tex]
The product is -60
a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length og the hypotenuse if the triangle? round to the nearest tenth.
Answer:
4.06 in.
Step-by-step explanation:
4
sin(80)= ---------- multiply by X
x
x* sin(80)= 4 divide by sin(80)
4
X=------------- simplify
sin(80)
X= 4.06 in.
Answer:
The length of the hypotenuse is 4.1 in
Step-by-step explanation:
By definition, the sine of an angle is:
[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]
In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.
With this information we can find the length of the hypotenuse h
[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]
Finally the length of the hypotenuse is 4.1 in
Four loan balances are $6,500, $3,600, $5,400, and $7,500, respectively. The current interest rates for the loans are 7%, 5%, 6%, and 9%, respectively. If the four are to be consolidated into one loan, what is the WEIGHTED AVERAGE interest rate on that loan?
A) 6.75%
B) 7.01%
C) 7.04%
D) 7.10%
[(455 + 180 + 324 + 675)/(65 + 36 + 54 + 75)] = 7.10
Answer is D.
Answer:
7.10% is the answer.
Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and what is the value of this maximum?
f(x), and the maximum is 3.
g(x), and the maximum is 5.’
f(x), and the maximum is 2.
g(x), and the maximum is 2.
Answer:
g(x), and the maximum is 5
Step-by-step explanation:
for given function f(x), the maximum can be seen from the shown graph i.e. 2
But for the function g(x), maximum needs to be calculated.
Given function :
g (x) = 3 cos 1/4 (x + x/3) + 2
let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)
g(x)= 3 cos1/4(0 + 0) +2
= 3cos0 +2
= 3(1) +2
= 3 +2
= 5 !
The floor of a bedroom is 12 feet by 15 feet and the walls are 7 feet high. One gallon of paint covers 250 square feet. How many gallons of paint do you need to paint the walls and the ceiling of the bedroom?
Calculate the total wall and ceiling area, then determine the number of gallons of paint needed using the given coverage per gallon.
To calculate the total wall and ceiling area:
Calculate the total wall area: (2 x 12 x 7) + (2 x 15 x 7) = 168 + 210 = 378 square feet.
Add the ceiling area: 12 x 15 = 180 square feet.
Sum the wall and ceiling areas: 378 + 180 = 558 square feet.
To determine how many gallons of paint:
Divide the total area by the coverage of one gallon: 558 ÷ 250 = 2.232 gallons (round up to ensure enough paint).
You would need approximately 2.232 gallons of paint to paint the walls and ceiling of the bedroom.
To find the total area that needs to be painted, we first calculate the area of the walls and the ceiling.
1. Area of the walls:
The bedroom has four walls, two of which are 12 feet by 7 feet and the other two are 15 feet by 7 feet.
Total area of the walls = 2(12 * 7) + 2(15 * 7) = 2(84) + 2(105) = 168 + 210 = 378 square feet
2. Area of the ceiling:
The ceiling is the same size as the floor, which is 12 feet by 15 feet.
Area of the ceiling = 12 * 15 = 180 square feet
3. Total area to be painted:
Total area = Area of walls + Area of ceiling = 378 + 180 = 558 square feet
4. Gallons of paint needed:
Since one gallon of paint covers 250 square feet, we divide the total area by the coverage of one gallon:
Gallons needed = Total area / Coverage per gallon = 558 / 250 ≈ 2.232 gallons
Therefore, you would need approximately 2.232 gallons of paint to paint the walls and ceiling of the bedroom.
What transformation was not done to the linear parent function, f(x) = x, to get the function [tex]g(x) = -\frac{1}{2}(x-3)+7[/tex]?
A. Shifted left 3 units
B. Vertically compressed by a factor of 2
C. Reflected over the x-axis
D. Shifted up 7 units
Answer:
The transformation was not done is Shifted left 3 units
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from
the x-axis
- A vertical compression is the squeezing of the graph toward
the x-axis.
- if k > 1, the graph of y = k•f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k.
- if 0 < k < 1 (a fraction), the graph is f(x) vertically compressed
by multiplying each of its y-coordinates by k.
- if k should be negative, the vertical stretch or compress is
followed by a reflection across the x-axis.
* now lets solve the problem
∵ f(x) = x
∵ g(x) = -1/2 (x - 3) + 7
# -1/2 means the graph is vertically compressed by a factor of 2
and reflected over the x-axis
# x - 3 means the graph shifted to the right 3 units
# + 7 means the graph shifted up 7 units
* The transformation was not done is Shifted left 3 units
Hi, please help!
Isaiah has worked 50 hours this week at a grocery store. For the first 40 hours, he gets paid $12 an hour. For any additional hours, Isaiah gets paid overtime at 1.5 times his base pay per hour. How much will Isaiah earn this week?
a. $600
b. $750
c. $660
d. $720
Isaiah will earn $660 for the 50 hours he worked
Answer:
c. $660
Step-by-step explanation:
rewrite the following biconditional as two conditionals:
A quadrilateral is a parallelogram if and only if it has two pairs of opposite sides that are parallel.
Answer:
If it has two pairs of opposite sides that are parallel, then a quadrilateral is a parallelogram.If quadrilateral is a parallelogram, then it has two pairs of opposite sides that are parallel.Step-by-step explanation:
One of the conditions has the condition and the conclusion written in one order; the other has them written in the opposite order.
If it has two pairs of opposite sides that are parallel, then a quadrilateral is a parallelogram.If quadrilateral is a parallelogram, then it has two pairs of opposite sides that are parallel.A fruit stand has to decide what to charge for their produce. They need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 oranges. We put this information into a system of linear equations.
Answer:
3.30 for apple and 2.00 for an orange
Step-by-step explanation:
To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. We can then solve this system using the elimination method to find the cost of an apple and an orange.
Explanation:To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. Let's use x to represent the cost of an apple and y to represent the cost of an orange.
From the given information, we can set up the following equations:
111x + 111y = 5.30
111x + 222y = 7.30
Next, we can solve this system of equations by using substitution or elimination. Let's use the elimination method:
Multiply the first equation by 2, and multiply the second equation by 1:
222x + 222y = 10.60
111x + 222y = 7.30
Subtract the second equation from the first:
111x = 3.30
Divide both sides by 111:
x = 0.03
Substitute this value back into either equation to solve for y:
111(0.03) + 222y = 7.30
3.33 + 222y = 7.30
222y = 3.97
y = 0.01
Therefore, the cost of an apple is $0.03 and the cost of an orange is $0.01 at the fruit stand.
Twice the difference of a number And 6 equals 5
Answer:
8.5
Step-by-step explanation:
Twice the difference of a number and 6 equals 5 is written algebraically as 2(x-6)=5, where x is the number. Solving for x:
2(x-6)=5
(x-6)=5/2
x=6+5/2
x=17/2
So the number is 17/2, or, expressed as a decimal number, 8.5
We solve the equation 'Twice the difference of a number and 6 equals 5' by identifying variable 'x' as the unknown number, rearranging the equation, and then performing a series of number operations (multiplication, addition, and division) to find x = 8.5.
Explanation:In the given problem, you are asked to solve for a number in the equation 'Twice the difference of a number and 6 equals 5'. We denote the unknown number we’re looking for as ‘x’. Thus, the equation becomes 2(x - 6) = 5.
By solving this equation step-by-step, we first distribute the 2 to both terms in the parentheses. This key step gives us 2x - 12 = 5.
Next, we add 12 to both sides to isolate 2x on the left side, which gives 2x = 17.
Finally, we divide both sides by 2 to solve for x, giving us x = 17 / 2 or 8.5.
In conclusion, the unknown number x that satisfies the condition 'Twice the difference of a number and 6 equals 5' is 8.5.
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The ratio of students who walk home from school to the students who ride the bus home is 2 : 7. The number of bus riders is how many times the number of students who walk home?
Answer:
3.5
Step-by-step explanation:
7/2=3.5
Answer:
3.5
Step-by-step explanation:
Ratio of
those who walk : those who ride = 2 : 7
This means that for every 2 students who walk, there are 7 students who ride
Therefore, for every 1 student that walks, (hypothetically) there are 3.5 (7/2) students who ride
Then the number of bus riders is 3.5 times the number of students that walk.
A circle with center D(0, -6) passes through the point C(5, -1). Use the Pythagorean Theorem to find the length of the circle’s radius, .
=
Answer:
Length of radius = [tex]5\sqrt{2}[/tex]
Step-by-step explanation:
The radius of the circle is the distance between the center and the point on the circle given.
The distance formula is [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Where
x_1 = 0
y_1 = -6
and
x_2 = 5
y_2 = -1
plugging these into the formula we get:
[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(-1-(-6))^2+(5-0)^2} \\=\sqrt{(-1+6)^2+(5)^2} \\=\sqrt{5^2 + 5^2} \\=\sqrt{50} \\=5\sqrt{2}[/tex]
Answer:
The radius of circle = 5√2 units
Step-by-step explanation:
Points remember
Distance formula:-
Let (x₁, y₁) and (x₂, y₂) be the two points, then the distance between these two points is given by
Distance = √[(x₂ - x₁)² + (y - y₁)²]
It is given that, center of circle (0, -6) and passes through (5, -1)
To find the radius of circle
Here (x₁, y₁) = (0, -6) and (x₂, y₂) = (5, -1)
Radius r = √[(x₂ - x₁)² + (y - y₁)²]
= √[(5 - 0)² + (-1 - -6)²]
= √(5² + 5²) = √(25 + 25) = √50 = 5√2 units
Therefore radius of circle = 5√2 units
How do you find the center and the radius for [tex]x^{2} +y^{2} =25[/tex]?
Answer:
The center is (0,0) and the radius is 5
Step-by-step explanation:
To find the center of a circle, you need to look at the equation
In this case this equation could be written as
[tex](x-0)^2+(y-0)^2=5^2[/tex]
The x value is x=0 for the center and the y values is y=0
The radius can be found by looking at the constant that is squared, so r=5
In the case of an equation like this
[tex](x-1)^2+(y+1)^2=3^2[/tex]
The center point would be (1,-1) and r=3
A rectangle with an area of 4/7 m2 is dilated by a factor of 7. What is the area of the dilated rectangle
according to the picture we have:
x.y=4.7
(7)x(7)y=49xy=(49)(4.7)=230.3
27) A man on the third floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet, what is the angle of elevation (in degrees) between the person on the street and the person in the building?
A) 15°
B) 30°
C) 45°
D) 60°
Answer:
Option B) 30°
Step-by-step explanation:
Given : A man on the third floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet.
To find : What is the angle of elevation (in degrees) between the person on the street and the person in the building?
Solution :
According to question, a rough diagram is framed which shows the position of man on street and man on building.
Refer the attached figure below.
A man on the third floor of a building is 25 feet up i.e. AB=25 feet.
The distance between the person on the street and the man in the building is 50 feet i.e. BC=50 feet.
We have to find the angle of elevation i.e. ∠C.
It form a right angle triangle,
Applying sin property of trigonometric,
[tex]\sin \theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]
[tex]\sin \theta=\frac{AB}{BC}[/tex]
[tex]\sin \theta=\frac{25}{50}[/tex]
[tex]\sin \theta=\frac{1}{2}[/tex]
[tex]\sin \theta=\sin 30^\circ[/tex]
[tex]\theta=30^\circ[/tex]
Therefore, Option B is correct.
The angle of elevation is 30°.
Answer:
Its B
Step-by-step explanation:
I just did the test.
Triangle DEF is a scale drawing of triangle ABC. Triangle DEF has side lengths of 12 inches.Triangle ABC has side lengths of 84 inches. What is the scale.
Answer:
The scale is 7
Step-by-step explanation:
Divide 12 from 84 to get the answer.
Hope this helps! :)
Answer:
Step-by-step explanation:
Determine whether the graph of f(x) is a sinusoid.
f(x) = sin 20x + cos 8x
Answer
b. No
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.
The function is
f(x) = sin(20*x) + cos(8*x)
Which can be seen in the picture below
We can notice that f(x) is a not sinusoid. It has periodic amplitudes, and the function has a period T = π/2
The maximum and minimum values are
Max = 1.834
Min = -2
Answer:
B
Step-by-step explanation:
no
a metric kilometer is used in the same context as which english unit of measure?
i believe the answer youre looking for is a mile
Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. modifyingbelow integral from nothing to nothing with upper c xyz font size decreased by 5 ds; c is the line segment from left parenthesis 0 comma 0 comma 0 right parenthesis to left parenthesis 1 comma 3 comma 6 right parenthesis
Parameterize [tex]C[/tex] by
[tex]\vec r(t)=(1-t)(0,0,0)+t(1,3,6)=(t,3t,6t)[/tex]
with [tex]0\le t\le1[/tex]. Then the line integral is
[tex]\displaystyle\int_Cxyz\,\mathrm dS=\int_0^1x(t)y(t)z(t)\left\|\frac{\mathrm d\vec r}{\mathrm dt}\right\|\,\mathrm dt[/tex]
[tex]=\displaystyle18\sqrt{91}\int_0^1t^3\,\mathrm dt=\boxed{\frac{9\sqrt{91}}2}[/tex]
The line integral over the path C from (0,0,0) to (1,3,6) can be converted into an ordinary integral by parameterizing the line segment and then substituting in the integral. The result of the integral amounts to 5.
Explanation:The given integral involves a line segment from (0,0,0) to (1,3,6). Our task is to convert this line integral to an ordinary integral.
The path C from (0, 0, 0) to (1, 3, 6) can be parameterized as r(t) = ti + 3tj + 6tk for 0 ≤ t ≤ 1. So, the dr = dt(i + 3j + 6k).
Substituting for ds in the integral, we get: ∫ r(t)dt from 0 to 1, which can be reduced to three separate integrals with respect to x, y, and z respectively: ∫xdx from 0 to 1, ∫3ydy from 0 to 1, and ∫6zdz from 0 to 1. Now these can be easily integrated.
So, the solution will be:
∫xdx from 0 to 1 = [x^2/2] from 0 to 1 = 1/2,
∫3ydy from 0 to 1 = [3y^2/2] from 0 to 1 = 3/2,
∫6zdz from 0 to 1 = [6z^2/2] from 0 to 1 = 3.
Adding these up gives the result of the original line integral, which is 5.
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There are 16 gifts under the Christmas tree. If 1 4 of them are for Chloe, how many gifts will Chloe receive? gifts
Answer: 4
Step-by-step explanation: If 1/4 of them are for Chloe, you'd divide 16 by 4 to find the answer. 16 divided by 4 equals 4.
Answer:
4
Step-by-step explanation:
There are 16 gifts under the tree, in which 1/4 is addressed to Chloe. To solve the amount she will get, Multiply 16 with 1/4:
16 x 1/4 = (16 x 1)/4 = 16/4 = 4
Chloe will receive 4 of those gifts.
~
A train travels 480 miles at a constant speed (x), in miles per hour. Write an equation that can be used to find the speed of the train, if the time to travel 480 miles is 6 hours. you do not need to solve the equation
Answer:
480 = x(6)
Step-by-step explanation:
Given in the question that,
distance travelled by the train = 480 miles
time taken by the train to travel 480 miles = 6 hours
Suppose speed of train = x miles/hour
Formula to use to drive the equation
distance = speed x time480 = x(6)
x = 480/6
x = 80 miles/hour
Christopher is analyzing a circle, y2 + x2 = 121, and a linear function g(x). Will they intersect?
Yes, at positive x coordinates
Yes, at negative x coordinates
Yes, at negative and positive x coordinates
No, they will not intersect
3rd : yes, at negative and positive x coordinates
Answer:
Yes, at positive x coordinates
Step-by-step explanation:
"Reduce Fractions to lowest terms"
6 divided by 3.66
Answer:
100/61 or 1.63934
Step-by-step explanation:
The reduced fractions of 6/3.66 to the lowest terms is 100/61.
How to reduce fractions to the lowest terms?To reduce a fraction to its lowest terms, divide the numerator and denominator by the greatest common factor.A fraction is in its lowest or simplest term when the numerator and denominator have no common factor other than 1.A fraction is reduced, simplified, or in the lowest terms if one is the only common factor of the numerator and denominator.⇒ 6/3.66 = 600/366 = 100/61.
Hence, the reduced fraction of 6/3.66 to its lowest terms is 100/61.
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Use the graph below to fill in the blank with the correct number:
f(0) = _______
Answer:
1
Step-by-step explanation:
We are given a graph, in which x is independent value and y is dependent on the value of x.
f(0) means that x = 0.
so,
we will see in the graph where the x = 0
Obviously it can be anywhere either on origin or on y-axis. The point mark on y-axis is when y = 1
The area of the circular base of a cylinder is 36π square units. The height of the cylinder is 2 units.
What is the lateral area of the cylinder? Express the answer in terms of π.
12π square units
24π square units
60π square units
72π square units
Answer: second option.
Step-by-step explanation:
The formula used for calculate the lateral area of a cylinder is this one:
[tex]LA=2\pi rh[/tex]
Where "r" is the radius and "h" is the height
The formula for calculate the area of a circle (which is the base of a cylinder) is:
[tex]A=\pi r^2[/tex]
Knowing the area of the base, you can solve for the radius:
[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]
Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:
[tex]LA=2\pi (6units)(2units)[/tex]
[tex]LA=24\pi\ units^2[/tex]
Answer:
24π square units (edge)
Step-by-step explanation:
Find the number of permutations of the first 10 letters of the alphabet, taking 3 letters at a time.
1040
980
720
630
Answer:
720
Step-by-step explanation:
The permutation looks like this for that set of data:
[tex]_{10}P_{3}[/tex]
and the formula to solve it like this:
[tex]_{10}P_{3} =\frac{10!}{(10-3)!}[/tex]
which simplifies down to
[tex]_{10}P_{3} =\frac{10!}{7!}[/tex]
Since every number less than 8 in the numerator cancels out with the denominator, we have
[tex]_{10}P_{3}=10*9*8[/tex]
which equals 720
If b=33.2 and B=61° find a (picture provided)
For this case we have to, by definition:
[tex]tg (B) = \frac {33.2} {a}[/tex]
This means that the tangent of angle B will be equal to the leg opposite the angle on the leg adjacent to the same angle.
Then, clearing to have:
[tex]a = \frac {33.2} {tg (61)}\\a = \frac {33.2} {1.80404776}\\a = 18.403060[/tex]
Rounding out the value of a we have:
[tex]h = 18.4[/tex]
Answer:
Option C
Answer:
The correct answer is option c. 18.4
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Tan θ = Opposite side/Adjacent side
From the figure we can see a right triangle triangle ABC
To find the value of a
It is given that, b=33.2 and B=61°
Tan 61 = opposite side/Adjacent side
Tan 61 = b/a
a = 33.2/Tan 61 = 18.4
Therefore the correct answer is option c. 18.4
There are two numbers, one is 7 more than twice the other. The sum of the numbers is 43. Make the equation to find the smaller number. Find the two numbers. Answer: If the smaller number is x, the equation will be . The numbers in ascending order are and .
Answer:
the numbers are 12, 31
Step-by-step explanation:
Evaluate. 12!/12!
A.) 0
B.) 1
C.) 12
12/12=1
answer is B) 1
Hope this helps chu
Answer:
B.) 1
Step-by-step explanation:
Let x = 12!
We have
x / x
Anything divided by itself = 1
PLEASE HELP! Answer the questions about Figure A and Figure B below.
I THINK that; Yes they are congruent but I don’t know the second parts. I think D is one of them. maybe B as well? Sorry