for the ahe area of triangle
Height of the triangle = 2 units, base= 5 unit
Area of triangle =1/2 Breadth x height
Susbtitute the value and simplify:
[tex]\begin{gathered} \text{ area of triangle=}\frac{1}{2}\times2\times5 \\ \text{ area of triangle= }5\text{ units} \end{gathered}[/tex]Answer =5 units
You invest $1000 in an account that has an annual interest rate of 4%, compounded quarterly for 12 years. How much money will you have after the 12 years? $3138.43 O $3237.27 O $1601.03 O $1612.23
The compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\times t}[/tex]where A is the resulting amount after t years, P is the present value (or principal amount) , r is the annual interest rate and n is the number of compounding periods per year.
From the given information, we have that
[tex]\begin{gathered} P=1000 \\ r=0.04 \\ n=4\text{ (quaterly=4 times per year)} \\ t=12\text{ years} \end{gathered}[/tex]By substituting these values into the formula, we have
[tex]A=1000(1+\frac{0.04}{4})^{4\times12}[/tex]which gives
[tex]\begin{gathered} A=1000(1.01)^{48} \\ A=1000(1.6122) \\ A=1612.226 \end{gathered}[/tex]Therefore, by rounding to the nearest thousandth, the answer is $1612.23, which corresponds to the last option.
Find the radius of the circle and the coordinates of its center
Hence, the radius of the circle is 10, and the coordinates of its centre is (6,-2)
The box plots below show the number of goals that two hockey players, Sam and Barry, Scored each season during their careers.Select all that are TRUE1) Barrys data is nearly symmetrical2) the median is Sams data is more than Barrys data3) Sam scored more goals in one season than berry did.4) Barrys chart shows more variable than Sams5) Sams distribution is skewed left
From the given distribution, it is clear that
Sam scored more goals in one season than berry did.
and
Barrys data is nearly symmetrical
How can you find the next digit in the quotient?
Bring down the ? to show there are 2 tens
? ones that still need to be divided.
Bring down the next digit 6 to show there are 2 tens and 6 ones that still need to be divided.
This method of dividing is called the long division method.
In this, we divide the dividend with the divisor and get a quotient and a remainder.
The steps involved are given below :
1. Take the dividend's first digit from the left. Determine whether this digit is bigger than or equal to the divisor.
2. Then divide it by the divisor and write the result as the quotient on top.
3. Subtract the result from the digit and record the difference in the box below.
4. Reduce the dividend by the following digit (if present).
5. Repeat the above steps.
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Select the equations below that are equivalent to -6 = -20 - v
Given
[tex]-6=-20-v[/tex]- For -72 = 9(-20 - v):
[tex]\begin{gathered} -\frac{72}{9}=\frac{9(-20-v)}{9} \\ -8=-20-v \end{gathered}[/tex]The equation is not equivalent
- For -90 = 15(-20 - v):
[tex]\begin{gathered} \frac{-90}{15}=\frac{15(-20-v)}{15} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 5 * -6 = -100 - 5v:
Common factor 5
[tex]\begin{gathered} -30=5(-20-v) \\ \frac{-30}{5}=\frac{5(-20-v)}{5} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 3 * -6 = -60 - 3v:
Common factor 3
[tex]\begin{gathered} -18=3(-20-v) \\ \frac{-18}{3}=\frac{3(-20-v)}{3} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
Answer:
-90 = 15(-20 - v)
5 * -6 = -100 - 5v
3 * -6 = -60 - 3v
Find the approximate area between the curve and the x-axis on the interval using 4 rectangles. Use the left endpoint of each rectangle to determine the height.
We have to approximate the area under the curve using the given rectangles.
Each rectangle will have an area that is equal to the width (the interval Δx) times the height (that is f(xi)).
We can express the formula for the approximation as:
[tex]A=\sum_{i=1}^4f(x_i)\cdot\Delta x=\sum_{i\mathop{=}1}^4f(x_i)(x_{i+1}-x_i)[/tex]We will have to calculate f(x) for x = 0, 4, 8 and 12, which are the left endpoints of the interval for each rectangle.
Given that f(x) is defined as:
[tex]f(x)=-2x^2+32x+5[/tex]we can calculate each value as:
[tex]f(0)=-2(0)^2+32(0)+5=5[/tex][tex]\begin{gathered} f(4)=-2(4)^2+32(4)+5 \\ f(4)=-2(16)+128+5 \\ f(4)=-32+128+5 \\ f(4)=101 \end{gathered}[/tex][tex]\begin{gathered} f(8)=-2(8)^2+32(8)+5 \\ f(8)=-128+256+5 \\ f(8)=133 \end{gathered}[/tex][tex]\begin{gathered} f(12)=-2(12)^2+32(12)+5 \\ f(12)=-288+384+5 \\ f(12)=101 \end{gathered}[/tex]We can now calculate the approximation as:
[tex]\begin{gathered} A=f(0)(4-0)+f(4)(8-4)+f(8)(12-8)+f(12)(16-12) \\ A=5(4)+101(4)+133(4)+101(4) \\ A=20+404+532+404 \\ A=1360 \end{gathered}[/tex]Answer: the approximation is equal to 1360 square units [Fourth option].
Solve -4x + 3 > 23 or 7x - 6 > 22
Answer:
-4x + 3 > 23 Answer is x<-5
Step-by-step explanation:
A rocket is launched straight up with a velocity of 8.36. What would be the velocity when it lands?
If the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
Given that the rocket is launched straight up with a velocity of 8.36.
We are required to find the velocity when the rocket lands.
Velocity is basically the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference.
When the velocity of rocket while it goes up is 8.36 then the velocity when it lands is also 8.36 because if the velocity will increase then the rocket will crash also.
Hence if the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
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0.149 divided 8,712
j
knjfjfjfjfjfjf help me solve this thanks !!
Answer:
132 degrees
Step-by-step explanation:
102+30 = 132
I need to factor this expression (7th grade math):26x + 18
SOLUTION:
Required: To factorize the expression:
Solving:
[tex]\begin{gathered} 26x\text{ + 18} \\ \text{First we find the GCF of each terms of the binomial. The greatest co}mmon\text{ factor betwe}en\text{ 26x and 18} \\ 2(13x\text{ + 9)} \end{gathered}[/tex]Final answer:
The final answer is 2(13x + 9)
The quadratic equation d = -t2 + 4t + 33 models the depth of water, d, in feet
in a flood channel t hours after a rainstorm.
a. Solve the equation -t2 + 4t+ 33 = 0.
b. Approximate the positive solution found in part (a) to two decimal
places.
c. Interpret the answer to part (b) in terms of the problem.
a. The solution of the equation is t = 2 ± √37.
b. The approximation of the positive solution is 8.08.
c. The interpretation is that the depth of the water is 0 feet after 8.08 hours of the rainstorm.
We are given a quadratic equation. The equation is given below :
d = -t² + 4t + 33
The equation models the depth of the water "d" in a flood channel "t" hours after a rainstorm.
a. We have to solve the equation :
-t² + 4t + 33 = 0
t² - 4t - 33 = 0
t = 2 ± √37
b. We need to approximate the positive solution found in part (a) to two decimal places. The positive solution is t = 2 + √37.
t = 2 + 6.08
t = 8.08
c. The depth of the water is 0 feet after 8.08 hours of the rainstorm.
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od 2 - 7th Grade Math) Simplify the following expressions: (9x + 3) - (5x - 7) (1 Point) Enter your answer
Simplifying the expression, we have:
[tex]\begin{gathered} (9x+3)-(5x-7) \\ =9x+3-5x+7 \\ =(9x-5x)+(3+7) \\ =4x+10 \end{gathered}[/tex]So the simplified expression is 4x + 10.
PLSSS!! Help me with this question I’ve been on it for hours!! Pls show decimal form or fraction form
Answer:
(6, 4)
Step-by-step explanation:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
= ((10 + 2)/2, (7 + 1)/2)
= (12/2, 8/2)
= (6, 4)
Answer:8.5 and 2.5
Step-by-step explanation:7, 8, MD 9, 10 There are four numbers in this sequence and MD is the midpoint. To find MD we have to find what is in the middle of 8 and 9. The number between them is 8.5 or
8 1/2(which is also 8 and one half)
For 2 and 1 same thing, what is between 2 and 1? To find that the number line goes 2, 2.9, 2.8, 2.7, 2.6, 2.5, 2.4, 2.3, 2.2, 2.1, and 1.
What is the midpoint in all of this? 2.5!Will someone please help me with this? I tried getting help but it didn’t work
Amrita wants to raise more than $200 for a charity by walking dogs in her neighborhood. She charges $7 per walk.What is an inequality that can be used to find the number of walks, w, that Amrita needs to complete?
Given:
Amrita wants to raise more than $200 for a charity.
She charges $7 per walk.
[tex]\begin{gathered} 7w>200 \\ \end{gathered}[/tex]need answer asap ty
multiplying integers
1. 13 + (-20) =
2.29 + (-12) =
3.21 + (-13) =
4.-19 + (-26) =
answer 1=-7
2=17
3=8
4=-45
Which letrero Best represents √27 on the number line.
You have the following number
√27
In order to determine which letter best represent the previous number, you take into account the following square roots:
√25 = 5
√36 = 6
Then, you can consider that √27 is a number in between 5 and 6, because √27 in anumber in between √25 and √36.
The only letter that is in between 5 and 6 on the number line, is the letter C.
Hence, letter C best represents √27
The slope of the line is given by the variable m. Slowly drag the m slider to the right. How does this changethe line?
2.
As you can see:
Rise = 2
Run = 2
Slope = 2
The water level in a lake was monitored and was noted to have changed −213 inches in one year. The next year it was noted to have changed −116 inches. What was the total change in the water level over the two years? Enter your answer as a simplified mixed number by filling in the boxes.
are those fractions??
Multiply. Simplify, you may leave the numerator and denominator in answer in factored form.
Step 1
Given;
Step 2
Multiply
[tex]\frac{x^3+1}{x^3-x^2+x}\times\frac{3x}{-15x-15}=\frac{3x^4+3x}{-15x^4-15x}[/tex]Simplify
[tex]\frac{3x\left(x+1\right)\left(x^2-x+1\right)}{-15x\left(x+1\right)\left(x^2-x+1\right)}=-\frac{1}{5}[/tex]Answer;
[tex][/tex]Use the long division method to find the result when 8x3 + 14x2 11x - 8 is divided by 2x + 1. If there is a remainder, express the result in the form q(a) +
Let's develop a synthetic division
As you can observe, the division is exact because its reminder is zero.
Hence, the answer is-
[tex]\frac{8x^3+14x^2-11x-8}{2x+1}=4x^2+5x-8[/tex]you invest 1,000 in an account that pays simple interest of 3% for 10 years. what is the amount of money you'll have at the end of the 10 years?
Given data:
The given principal is P=1,000.
The given rate of interest is r=3%.
The given time is t=10 years.
The expression for the final amount after 10 years is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=1,000+\frac{1,000\times3\times10}{100} \\ =1,300 \end{gathered}[/tex]Thus, the final amount after 10 years is 1,300.
Find the equation of the line with the following:slope = 2/5; passes through (-3, 1)
Answer:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]Explanation:
Given the slope and a point on the line, we use the point-slope form to find the equation of the line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{2}{5} \\ (x_1,y_1)=(-3,1) \end{gathered}[/tex]Substitute the given values:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{2}{5}(x-(-3)) \\ y-1=\frac{2}{5}(x+3) \\ y=\frac{2}{5}(x+3)+1 \\ y=\frac{2}{5}x+\frac{6}{5}+1 \\ y=\frac{2}{5}x+\frac{11}{5} \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]see imageThere were 400 people that tooka survey about quality ofrestaurants. 240 people said thatOutback was the beststeakhouse. What percent ofpeople said Outback was the beststeakhouse?
total people(TOTAL) : 400
People that said that the outback was the best ( BEST) : 240
percent of people said Outback was the best steakhouse : BEST / TOTAL : 240/400 = 0.6
Percent = 0
Solve the equation. Justify each step using the word bank provided. *Properties may be used more than once!
Given
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Combine
Like Terms
Justifications for each step:
2(x − 4) − 9 = 3(2x + 1) + 4
HELP PLEASE
The result of the equation 2(x − 4) − 9 = 3(2x + 1) + 4 by using the distributive property is x = -6
The equation is
2(x − 4) − 9 = 3(2x + 1) + 4
The distributive property states that multiplying the sum of two or more variables by a number will provide the same result as multiplying each variable individually by the number and then adding the products together.
The distributive property of the addition
A(B + C) = AB + AC
The distributive property of the subtraction
A(B - C) = AB - AC
The equation is
2(x − 4) − 9 = 3(2x + 1) + 4
Apply the distributive property
2x-8-9 = 6x+3+4
2x-17 = 6x+7
Rearrange the like terms and combine it
2x-6x = 7+17
-4x = 24
x = -6
Hence, the result of the equation 2(x − 4) − 9 = 3(2x + 1) + 4 by using the distributive property is x = -6
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helpppppppp ur gurlll out
Answer:
Step-by-step explanation:
2(x-3) + 21 = -3
So:
My first step is to open the brackets
2x - 6 + 21 = -3
Then I plus two numbers in the equation:
2x + 15 = -3
Third step is: 2x = -3 - 15
2x = -18
The value of x that makes the equation true is:
x = -18/2
x = -9
Robin and Dovey have four pet pigeons that they train to race. They release the birds at Robin's house and then drive to Dovey's to collect them. To drive from Robin's to Dovey's, because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south. How far do the pigeons have to fly to go directly from Robin's house to Dovey's house? Round your answer to the nearest tenth. (HINT: draw a picture!) *
Let the north and east with a positive sign, so, the south and west are negative signs
Because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south.
So, the resultant horizontal distance = 1.7 + 0.9 - 4.1 = -1.5 km
The resultant vertical distance = 3.1 + 2.3 + 1.2 - 0.4 = 6.2 km
So, the direct distance will be calculated using Pythagorean theorem :
So, the distance d =
[tex]\begin{gathered} d=\sqrt[]{(-1.5)^2+(6.2)^2}=\sqrt[]{2.25+38.44} \\ \\ d=\sqrt[]{40.69}=6.37887 \end{gathered}[/tex]Rounding the answer to the nearest tenth
so, the answer is : 6.4 km
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C (x) = 0,3x2 -96x+14,848. How many cars must be made to minimize the unit cost?Do not round your answer
Answer:
[tex]160\text{ cars}[/tex]Explanation:
Here, we want to get the number of cars to be made so as to minimize the unit cost
What we have to do here is to find the first derivative of the given cost function
Mathematically, we have that as:
[tex]C^{\prime}(x)\text{ = 0.6x -96}[/tex]To get the minimum x value, we simply set the first derivative to zero and solve for x
Mathematically, that would be:
[tex]\begin{gathered} 0\text{ = 0.6x-96} \\ 0.6x\text{ = 96} \\ x\text{ = }\frac{96}{0.6} \\ x\text{ = 160 } \end{gathered}[/tex]A jeweler has found that the monthly revenue received from selling a pair of earrings at a cost of d dollars each is given by the polynomial −7d2+180d. Find the monthly revenue received when d=17 dollars.
The monthly revenue is $1037
What is a linear equation in one variable?
A linear equation in one variable is equation whose degree is one and there is only one variable present.
We are given the monthly revenue received from selling a pair of earrings at a cost of d dollars is given by equation [tex]-7d^{2}+180d[/tex]
We have to find the monthly revenue received when the cost is $17
That is d=17
Now we substitute d=17 in the given equation to find the monthly revenue
We get,
[tex]-7d^{2}+180d\\[/tex]
⇒[tex]-7(17^{2})+180(17)\\[/tex]
⇒ -2023+3060
⇒1037
Hence the monthly revenue earned is $1037
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