Answer:
y = 3? (A) −192 ... If P = a² + a −1 and R = −a − 1, which expression represents P + R.
Step-by-step explanation:
A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?
A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?
we know that
The volume of the square prism is equal to
[tex]V=b^2\cdot h[/tex]where b is the length side of the square base and h is the height of the prism
The volume of the square pyramid is
[tex]V=\frac{1}{3}\cdot b^2\cdot h[/tex]Remember that
the volume of the square prism is 900in3
so
[tex]900=b^2\cdot h[/tex]substitute in the formula of volume of the pyramid
[tex]\begin{gathered} V=\frac{1}{3}\cdot b^2\cdot h \\ \\ V=\frac{1}{3}\cdot900 \\ V=300\text{ in\textasciicircum{}3} \end{gathered}[/tex]the volume of the pyramid is 300 cubic inchesSelect all of the scenarios below that correctly identify the independent variable. A. Charlie gets paid by the hour. The number of hours he works is the independent variable. B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable. C. How much Caleb weighs is relative to the amount he eats. The amount he weighs is the independent variable. D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
Independent varible are variable that dosent depend on any factor that afftect the scenarios.
the scenarios that identify the independent variable.
A. Charlie gets paid by the hour. The number of hours he works is the independent variable.
B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable.
D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
Find the radian measure of θ if θ is a central angle in a circle of radius r=14in and θ cuts off an arc length s=7π in
The formula for determining the length of an arc is experessed as
arc length = θ x r
where
θ is the central angle
r is the radius of the circle
From the information given,
arc length = 7π in
r = 14 in
By substituting these values into the formula,
7π in = θ x 14 in
We would divide both sides of the equation by 14 in. We have
7π in/14 in = θ x 14 in/14 in
θ = π/2
Write the standard form of the equation
1) through: (-5, 3) and (2,-2)
helppppppppppppppppppppppppppppppppppppppppp asapppppppppppppppppppppppppppppppp
Answer:
5
Step-by-step explanation:
((12*3)-(3*1/3))/((4*3-5))=
((36)-(1))/((12-5))=
(35)/(7)=5
Answer: it is going to be 35/7 = 5
The product of eight and a number b
Write a variable expression for the word phrase
What is the annual percentage yield (APY) for money invested at an annual rate of(A) 4.09% compounded monthly?(B) 4.1% compounded quarterly?
The annual percentage yield is given by the following formula:
[tex]\text{APY}=(1+\frac{r}{n})^n-1[/tex]Where r is the stated annual interest rate (in decimal form) and n is the number of times compounded.
A) APY for money invested at an annual rate of 4.09% compounded monthly.
Thus, the annual interest rate in decimal form is:
[tex]r=\frac{4.09\%}{100\%}=0.0409[/tex]And as it is compounded monthly then n=12.
Replace these values and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.0409}{12})^{12}-1 \\ \text{APY}=(1+0.0034)^{12}-1 \\ \text{APY}=(1.0034)^{12}-1 \\ \text{APY}=1.0417-1 \\ \text{APY}=0.0417 \end{gathered}[/tex]The APY is 0.0417=4.17%.
B) 4.1% compounded quarterly:
The annual interest rate is:
[tex]r=\frac{4.1\%}{100\%}=0.041[/tex]As it is compounded quarterly then n=4.
Replace and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.041}{4})^4-1 \\ \text{APY}=(1+0.0103)^{12}-1 \\ \text{APY}=(1.0103)^{12}-1 \\ \text{APY}=1.1302-1 \\ \text{APY}=0.1302 \end{gathered}[/tex]The APY is 0.1302=13.02%
A graden plot 4m by 12m has one side along the fence.The area of the garden is to be doubled by digging a border of uniform width on the other three sides.What should the width of the border be?
The width of the border is 6 m after digging a border of uniform width on the other three sides.
Step 1:
Original garden plot is 4 m by 12 m. The 12 m side is against the wall.
A border of length D is along three sides of the plot (the 4th side is the wall).
Step 2
area of original garden plot is 12 x 4 = 48 [tex]m^{2}[/tex]
area of new plot = 96 [tex]m^{2}[/tex] (twice the original plot)
96 = (4 + D) (12 + 2D)
Set up equation for the area of the new area of the new plot (double the area of the old garden plot).
Step 3
96 = (4 + D) (12 + 2D)
[tex]96 = 2d^{2}+12d+4(2d+12)[/tex]
[tex]96 = 2d^{2}+12d+8d+48[/tex]
[tex]96 = 2d^{2}+20d+48[/tex]
[tex]96 -2d^2-20d-48 = 0[/tex]
[tex]48-2d^2-20d = 0[/tex]
[tex]-2(d^2+10d-24) = 0[/tex]
d = -12
Now solve for D
Step 4
D = 6 meters
Ignore negative answer because border must be a positive number. So Border is -12 [tex]m^{2}[/tex] (6 m).
Hence the answer is the width of the border is 6 m after digging a border of uniform width on the other three sides.
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estimated sales volume =47.81+0.47(Advertising Expenditures)If the company has a target sales volume of $175,000,how much should the sales manager allocate for the advertising in the budget ? round your answer to the nearest dollar
We are given an estimate equation.
Let the estimate sales volume be "s" and advertising expenditure be "a".
The given equation is:
[tex]s=47.81+0.47a[/tex]The company has a target sales of 175,000, which is a value for "s".
To get how much they need to allocate for advertising, we can solve for "a" in the equation and substitute the "s" value with 175,000:
[tex]\begin{gathered} s=47.81+0.47a \\ 47.81+0.47a=s \\ 0.47a=s-47.81 \\ a=\frac{s-47.81}{0.47} \end{gathered}[/tex]Now we substitute 175,000 into "s":
[tex]a=\frac{175,000-47.81}{0.47}=\frac{174,952.19}{0.47}=372,238.7021\ldots\approx372,239[/tex]So, by the equation estimate, the sales manager should allocate $327,239 for advertising.
How do I get the answers to thisQuestion 1 - 4
Answer:
Lines d and e are parallel and lines s and t are also parallel
1. Alternate Exterior Angles Theorem
2. Corresponding Angles Postulate
3. Alternate Angles Postulate
4. Co-interior Angles Theorem
Explanation:
Given the below;
1. Given that;
[tex]\angle1\cong\angle4[/tex]The theorem that justifies the above is the Alternate Exterior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
2. Given that;
[tex]\angle2\cong\angle3[/tex]The theorem that justifies the above is the Corresponding Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the corresponding angles are congruent.
3. Given that;
[tex]\angle6\cong\angle7[/tex]The theorem that justifies the above is the Alternate Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate angles are congruent.
4. Given that;
[tex]m\angle5+m\angle8=180[/tex]The theorem that justifies the above is the Co-interior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, angles that are in the same similar position are supplementary, that is, they add up to 180 degrees.
How many one and one-sixths are in five and five-sixths?
Using operations of fractions, the answer obtained is
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
What is fraction?
Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator,
Let there are x [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
[tex]1\frac{1}{6} x = 5\frac{5}{6}\\\frac{7}{6}x = \frac{35}{6}\\x = \frac{35}{6} \times \frac{6}{7}\\x = 5[/tex]
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
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EUREKA M
3. Give an example of a scale factor that produces an enlargement. Explain why you chose this
scale factor.
on. Explain why you chose this
scale factor.
We will take an example of a rectangle with a scale factor of enlargement by 2.
For example, consider a rectangle with dimensions of 6 cm and 3 cm.
If we increase the scale factor for the initial rectangle by 2, both sides of the rectangle will be doubled. By raising the scale factor, we mean multiplying the present rectangle measurement by the supplied scale factor. We have multiplied the original rectangle measurement by 2 here.
The rectangle's length was originally 6 cm and its width was 3 cm.
After multiplying by two, the length is 12 cm and the width is 6 cm.
Thus, we took an example of a rectangle with a scale factor of enlargement by 2. We consider this for a better understanding.
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What is an equation of the line that passes through the points (2, 2) and
(1, -2)
Answer: y = 4x + -6
Step-by-step explanation:
Find a pair of adjacent angles:4 and 14Find a pair of vertical angles:233 and 21)
SOLUTION
By definition, adjacent angles are (of a pair of angles) formed on the same side of a straight line when intersected by another line.
Vertical Angles are the angles opposite each other when two lines cross.
Going by this above definition, a pair of adjacent angles in the figure in Q1 are:
4 and 2.
Going by this above definition, a pair of vertical angles in the figure in Q1 are:
3 and 2.
It Carlos sits 3 feet from the fulcrum of a see-saw, how far from the fulcrum must his baby-sister who weighs three-times his weight sit?
A. 1 foot
B. 6 feet
C. 3 feet
D. 9 feet
Answer: B: 6 feet
Step-by-step explanation: To solve this problem, we need to use the concept of leverage, which is the force applied to an object at a distance from its pivot point. In this case, Carlos is applying a force of 3 feet from the fulcrum, while his baby sister is applying a force 3 times as large, at a distance from the fulcrum.
To find the distance from the fulcrum that the baby sister must sit, we need to balance the forces applied by Carlos and his sister. This means that the product of the force applied by Carlos and the distance from the fulcrum must be equal to the product of the force applied by his sister and the distance from the fulcrum where she must sit.
We can use this information to write the equation: 3 * 3 = 3 * x
Where x is the distance from the fulcrum where the baby sister must sit. We can solve for x by dividing both sides of the equation by 3 to get: x = 6
Therefore, the baby sister must sit 6 feet from the fulcrum in order to balance the forces applied by Carlos and his sister. The correct answer is B. 6 feet.
What is the third term of the recursive sequence below
Given the sequence:
[tex]\begin{gathered} a_1=-6 \\ a_n=\frac{1}{2}a_{n-1}-n \end{gathered}[/tex]Let's find the third term of the sequence.
To find the third term, a3, we have:
First find the second term, a2:
[tex]\begin{gathered} a_2=\frac{1}{2}a_{2-1}-2 \\ \\ a_2=\frac{1}{2}a_1-2 \\ \\ a_2=\frac{1}{2}(-6)-2 \\ \\ a_2=-3-2 \\ \\ a_2=-5 \end{gathered}[/tex]The second term is -5.
To find the third term, we have:
[tex]\begin{gathered} a_3=\frac{1}{2}a_{3-1}-3 \\ \\ a_3=\frac{1}{2}a_2-3 \\ \\ a_3=\frac{1}{2}(-5)-3 \\ \\ a_3=-2.5-3 \\ \\ a_3=-5.5 \end{gathered}[/tex]Therefore, the third term of the
What two numbers add to give 3 and multiply to give -18
Find g(x), where g(x) is the translation 5 units left of f(x) =3(x+5)^2 -7
The rule for the translated function is:
g(x) = 3*(x + 10)^2 - 7
How to find the rule for g(x)?
First, we know that for a function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.
if N < 0, the translation is to the right.
A translation of 5 units to the left is written as:
g(x) = f(x + 5)
Replacing f(x) we get:
g(x) = 3*(x + 5 + 5)^2 - 7
g(x) = 3*(x + 10)^2 - 7
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if gh=53 and hi=7 then gi=
In the given line, the length of the line gi is 60 units.
What is a line?A line is an indefinitely long, straight object that is drawn with a minimum width in geometry but is said to have no specific width in mathematics since it lacks depth.An angle is created when two straight lines or rays intersect at a single terminal. The vertex of an angle is the location where the two rays meet.So, the length of gi will be:
We know that,
gh = 53hi = 7Now, we can easily see that the given line is:
gi = gh + higi = 53 + 7gi = 60Therefore, in the given line, the length of the line gi is 60 units.
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Tic, Tac and Toe are siblings. Toe is Tic and Tac's brother
but Tic is not Toe's brother. How is Tic related to Toe?
Answer: Tic is either Toe's brother or sister.
Step-by-step explanation: There's really no explanation. It's just outside the box thinking.
How to find the GCF of 65,39,and 13
Answer:
13
Step-by-step explanation:
65 ÷ 13 = 5
39 ÷ 13 = 3
13 ÷ 13 = 1
(All can be divided by 13 so the GCF is 13)
Given the end points of A(-8,-2) and B(6,19). The segment AB is divided into the ratio atAR:RB in a 2:5 ratio. Find the coordinates of point R.R=
The given coordinates in the question are
[tex]\begin{gathered} A=(-8,-2)\text{ = x1=-8, y1=-2} \\ B=(6,19)\text{ = x}2=6,y2=19 \end{gathered}[/tex]Let the coordinate at R be
[tex]R=(x,y)[/tex]The ratio of the line segment given is
[tex]AR\colon RB=2\colon5\text{ (m=2,n=5)}[/tex]The formula to calculate the coordinate of a line segment in a given ratio is given below as
[tex](x,y)=(\frac{mx_2+nx_1}{m+n}),(\frac{my_2+ny_1}{m+n})[/tex][tex]undefined[/tex]Horatios haunted house
The ratio of screamers to runners are 4:6 and 10:15.
Given,
the ratio of customers who screams and customers who run away is 2:3
Let
number of screamers be 'x'
number of runners be 'y'
To find number of screamers we can solve the ratio in proportion,
[tex]2:3::x:6\\\frac{2}{3}=\frac{x}{6}\\ \frac{2*6}{3}=x\\ 4=x[/tex]
Verify: [tex]4:6=2:3[/tex]
To find number of runners we can solve the ratio in proportion,
[tex]2:3::10:y\\\frac{2}{3}=\frac{10}{y}\\ {y}=\frac{3*10}{2}\\ y=15[/tex]
verify:[tex]10:15=2:3[/tex]
Hence, the ratio of screamers to runners are 4:6 and 10:15.
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In the equation (x + 4)^2 = 49, if x equals 3 what is another solution for x?
Please answer quickly.
Only 1 and 2 pls helppp
Answer:
See the attached image for work.
1) The slope is 4.
2) The slope is 2.
Answer:
on the first one the rise is 20 and the run is 5. 5 divided by 20 is 4 so the slope is 4. I haven't answered the second one yet, sorry.
help meeeeeeeeee pleasee
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
Sel 9.5.37 Assigned Media Question Help D You, a A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 17 feet more than the length of the shortest side. Find the dimensions if the perimeter is 153 feet. What is the length of the shortest side?
First we can set the equations we already know
[tex]a\text{ +b +c = 153 ft}[/tex]Where a, b and c are the sides of the triangle. Then, I will assign "a" the shortes side. One side is twice the shortest side so:
[tex]b\text{ = 2a }[/tex]Now, the sentence says, the third side is 17 feet longer that the shortes side "a":
[tex]c\text{ = a + 17}[/tex]Now we have a system of three equations with three unknown variables, so it will be easy to find the value of all the variables. If we put "b" and "c" in the first equation we have:
[tex]a\text{ + (2a) + (a+17) = 153 ft}[/tex][tex]\begin{gathered} 4a\text{ = 153-17} \\ 4a\text{ = }136 \\ a\text{ = 136/4} \\ a=34 \end{gathered}[/tex]Now, since we assigned "a" as the shortest side, we are done.
The bull in Ms. Garcia's pasture weighs 0.95 tons. What is the weight of the bull in pounds?
Answer:
The bull weighs 1,900 pounds.
Step-by-step explanation:
2,000 pounds = 1 ton
0.95 x 2,000 = 1,900 pounds
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Answer: 1,900 pounds
Step-by-step explanation:
There are 2,000 pounds in a ton, so we will multiply 0.95 tons by 2,000 to figure out the weight of the bull in pounds.
0.95 * 2,000 = 1,900 pounds
What's the length of the hypotenuse of a right triangle if the length of one leg is 7 units and the length of the other leg is 14 units?
ANSWER:
The hypotenuse is
[tex]7\sqrt[]{5}=15.65[/tex]STEP-BY-STEP EXPLANATION:
In this case we can calculate the value of the hypotenuse by means of the Pythagorean theorem.
[tex]\begin{gathered} h^2=a^2+b^2 \\ a=7 \\ b=14 \end{gathered}[/tex]replacing
[tex]\begin{gathered} h^2=7^2+14^2 \\ h^2=49+196 \\ h=\sqrt[]{245} \\ h=7\sqrt[]{5}=15.65 \end{gathered}[/tex]–5 = –3(h − 10) + –8
Answer:
h = 9
Step-by-step explanation:
-5 = -3(h - 10) + (-8)
−5 = −3h + 22
−3h + 22 = −5
−3h = −27
h = 9
--------------
check
-5 = -3(9-10)+(-8)
-5 = -27 + 30 - 8
- 5 = -5
the answer is good