3x2 - 13x - 10
multiplying the first and third terms we have
-30x2
The factors of -30 that will be added to get - 13 are -15 and 2
so we split the expression further
= 3x2 - 15x + 2x - 10
= 3x (x - 5) + 2 (x - 5)
= (x -5)(3x + 2)
8 As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E. С
From the rectangle given, we see the diagonals of the rectangle bisect each other at E.
From the properties of a rectangle is that;
1) The diagonals are congruent. That is, they are equal. AC = BD
2) The diagonals bisect each other into two equal parts.
These are the two properties we will use in solving the question
[tex]undefined[/tex]do 11, 9 ,17 make a triangle
We use the followig property of triangles:
• One side cannot be equal or greater than the sum of the other two sides
The sides of this triangle are: 11, 9 and 17.
The sum of the first two sides is: 11+9=20
The sum of the two sides is greater than the other remaining side (17).
Thus, 11, 9 and 17 do not make a triangle.
The population of a small town is said to be decreasing exponentially at a rate of 2% every year. In the year 2020 the population is 24,597.If this rate continues what is the expected population in the year 2025? Round your answer to the nearest whole number
Using exponential function to calculate the exponential decrease, the population in 2025 is 22278
Exponential FunctionAn exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on. Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
We can write the function as
A = N(1 + r)⁻ˣ
x = timer = rateN = initial valueLet's plug in our values and solve
A = 24597(1 + 0.02)⁻⁵
A = 22,278
The population in 2025 is 22278
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The area of a playground is 154 yd ^2. The width of the playground is 3 yd longer than its length. FInd the length and width of the playground.
Answer:
The length of the playground = 11 yards
The width of the playground = 14 yards
Explanation:
Let the length of the playground = l yd.
The width of the playground is 3 yd longer than its length.
Therefore, the width of the playground = (l+3) yd
Area of a Rectangle = Length x Width
Substituting the given values, we have:
[tex]154=l(l+3)[/tex]We then solve the equation above for l.
[tex]l^2+3l-154=0[/tex]We factorize:
[tex]\begin{gathered} l^2+14l-11l-154=0 \\ l(l+14)-11(l+14)=0 \\ (l-11)(l+14)=0 \\ l-11=0\text{ or l+14=0} \\ l=11\text{ yards, }l\neq-14 \end{gathered}[/tex]The length of the playground = 11 yards
The width of the playground = 14 yards
What are the first five terms of the arithmetic sequence defined explicitly by the formula an=14 - 3n
11, 8, 5, 2, -1
Option D is correct
Explanation:The given arithmetic sequence is:
[tex]a_n=14-3n[/tex]For the first term, substitute n = 1 into the arithmetic sequence
[tex]\begin{gathered} a_1=14-3(1) \\ a_1=14-3 \\ a_1=11 \end{gathered}[/tex]For the second term, substitute n = 2 into the arithmetic sequence
[tex]\begin{gathered} a_2=14-3(2) \\ a_2=14-6 \\ a_2=8 \end{gathered}[/tex]For the third term, substitute n = 3 into the arithmetic sequence
[tex]\begin{gathered} a_3=14-3(3) \\ a_3=14-9 \\ a_3=5 \end{gathered}[/tex]For the fourth term, substitute n = 4 into the arithmetic sequence
[tex]\begin{gathered} a_4=14-3(4) \\ a_4=14-12 \\ a_4=2 \end{gathered}[/tex]For the fifth term, substitute n = 5 into the arithmetic sequence
[tex]\begin{gathered} a_5=14-3(5) \\ a_5=14-15 \\ a_5=-1 \end{gathered}[/tex]Therefore, the first five terms are:
11, 8, 5, 2, -1
5. The circle graph shows the favorite music genre of radio listeners. Which of the following 2 categories combinedmake up the biggest percentage?Music PreferenceClassical 10%a. Alternative and classicalb. Country and rock15%AlternativeRock 35%C.Jazz and countryCountry25%Jazz 15%d. Rock and Classical
rock with 35% and country with 25% are the highest percentages, therefore the answer is: B
given BD and AC bisects each other. prove AB\\ CD
From step #6, AB is congruent to CD by CPCTC or Corresponding Parts of Congruent Triangles are Congruent.
Triangles ABE and CDE are congruent by SAS postulate.
Therefore, angle B and angle D are congruent.
Note that the segment BD is a transversal line that cuts AB and CD, and angle B and angle D are alternate interior angles.
The answer is :
XY || WZ ⇒ AB || CD
with a reason of :
Parallel lines cut by a transversal form congruent alternate interior angles.
A sinking fund is established to discharge a debt of $70,000 in 10 years. if deposits are made at the end of each 6-month period and interest is paid at the rate of 9%, compounded semiannually, what is the amount of each deposit? (round your answer to the nearest cent.)
The amount of each deposit is $210000
What is compound interest?Compound interest is when you reinvest your income. Compound interest distinctively means "interest on interest" and is the reason so many investors are so successful.
The computation of the each deposit is shown below:
Given that
Future value be $70,000
Time period = 10 × 2 = 20
And, the rate = 9% ÷ 2 = 4.5%
Now the formula is as follows
= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1
= ($70,000 × 4.5) ÷ (1 + 0.025)²⁰⁻¹
= $315,000 ÷ 1.5
= $210000
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The triangle has the sides AB = 4cm BC = 6cm AC = 8cmCalculate the triangles highest corner
Given: A triangle ABC with sides, AB= 4cm
BC=6cm and
AC=8cm
Required: To find out the triangle's highest corner.
Explanation: Let us first draw a triangle with given sides,
Petrol has a density of: 740 kg/m³ A container holds 12 litres of petrol. One litre is equal to 0.001 m³. What is the mass of the petrol?
The mass of the petrol is 8.88 kg.
Given, Petrol has a density of 740 kg/m³.
A container holds 12 litres of petrol.
One litre is equal to 0.001 m³.
As, Density = Mass/Volume
1 litre = 0.001 m³
12 litres = 0.012 m³
Now, using the formula, we get
740 = mass/0.012
mass = 740×0.012
mass = 8.88 kg
Hence, the mass of the petrol is 8.88 kg.
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Sarah is going to invest $79,000 and leave it in an account for 7 years. Assuming the
interest is compounded quarterly, what interest rate, to the nearest tenth of a
percent, would be required in order for Sarah to end up with $121,000?
The interest rate that would be required in order for Sarah to end up with $121,000 is R=6.1%
What is meant by compound interest?Compound interest, often known as interest on principal and interest, is the adding of interest to the loan or deposit principal. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest. Finance and economics both use compound interest frequently.
compound interest allows for the accumulation of interest from prior periods.
Given that Sarah is going to invest $79,000 and leave it in an account for 7 years.
We have to assume that the interest is compounded quarterly then,
A=P[tex](1+(R/400))^{4n}[/tex]
121000=79000[tex](1+(R/400))^{28}[/tex]
(121000/79000)=[tex](1+(R/400))^{28}[/tex]
[tex](1.53)^{1/28}[/tex]= [tex](1+(R/400))[/tex]
1.0153=[tex](1+(R/400))[/tex]
0.0153=R/400
R=6.1372
R=6.1%
Therefore, the interest rate is R=6.1%
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The relationship between the time you see lightning and the time you hear thunder is directly proportional to the distance the lighting is from where you are standing. Josh counted 12 seconds between seeing the lightning and hearing the thunder, and he knew that the lightning was about 5 miles away. If he counted 7 seconds between the next flash of lightning and thunder, about how far away was the lightning? Round to the nearest whole number.
Step 1: For solving this exercise, we need to know the speed of sound. We will calculate it this way:
Speed = Distance/Time
Replacing with the values Josh has.
Speed = 5 miles/12 seconds
Speed = 0.417 miles per second
Step 2: Now, let's calculate the distance after 7 seconds:
Using the same formula, we can find the distance, as follows:
Distance = Speed * Time
Distance = 0.417 * 7
Distance = 2.919
Distance = 3 miles (Rounding to the nearest whole number)
Step 3: Interpretation of the answer, as follows:
The lightning was 3 miles away when Josh counted 7 seconds between the next flash of lightning and thunder.
help please! will give brainliest
Answer:
I believe the top is 50 because 50 is the b value while the bottom would be 25 because that is the ac value of the expression
Step-by-step explanation:
above
Blake works at a grocery store and is paid every two weeks. He earned $486.50 this week. His pay will increase by 10% next week. What will his total
pay be for the two week period?
Answer:
$1,021.60
Explanation:Blake earn $486.50 in 1 week.
"The next week, his pay will increase by 10%"
2 weeks:
= $486.50 * 1.10(+10%)
= $535.15
Blake paid after two weeks. He got
= $486.50 + $535.10
= $1,021.60
Find the equation of the line passing through the given pair of points. Write the equation in slope-intercept form.(-4,-2), (3,7)
Equation of a line in slope intercept form:
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
To find the slope use the two given points in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{points: }(-4,-2)(3,7) \\ \\ m=\frac{7-(-2)}{3-(-4)} \\ \\ m=\frac{7+2}{3+4}=\frac{9}{7} \end{gathered}[/tex]Use the slope and one of the points to find the y-intercept:
[tex]\begin{gathered} y=mx+b \\ (3,7) \\ \\ 7=\frac{9}{7}(3)+b \\ \\ 7=\frac{27}{7}+b \\ \\ 7-\frac{27}{7}=b \\ \\ b=\frac{49-27}{7} \\ \\ b=\frac{22}{7} \end{gathered}[/tex]Then, the equation of the line passing through the given pair of points is:
[tex]y=\frac{9}{7}x+\frac{22}{7}[/tex]PLEASE ITS URGENT I MEED HELP AND PLEASE SHOW THE STEPSSSS
I WILL MARK BRIANLIEST OBVIOUSLY!
Answer:
KM = √53
Step-by-step explanation:
K is at (-4, 8), and M is at (-2, 1).
KM
[tex] \sqrt{ {( - 4 - ( - 2))}^{2} + {(8 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 2)}^{2} + {7}^{2} } = \sqrt{4 + 49} = \sqrt{53} [/tex]
Read the problem, set up a
multi-step equation with variables
on both sides, then solve ll.
#3
Mark is buying Christmas presents for members of his
family. He wants to spend $10 less on his brother than
he spends on his sister, and six dollars more than twice
the amount he spends on his sister on his wife. If Mark
has $100 to spend, how much does he intend to spend on
his brother?
HERE'S A Use the variable, s. for the
HINT
amount he will spend on
his sister.
Insert image of work here:
The amount spent on brother is $16, on sister is $26 and that on wife is $58.
According to the question,
We have the following information:
Mark is buying Christmas presents for members of his family. He wants to spend $10 less on his brother than he spends on his sister, and six dollars more than twice the amount he spends on his sister on his wife. And Mark
has $100 to spend.
Let's take the amount spent on sister to $s.
Amount spent on brother = $(s-10)
Amount spent on wife = $(6+2s)
So, we have the following expression:
s+s-10+6+2s = 100
4s-4 = 100
4s = 104
s = 104/4
s = $26
Amount spent on brother = 26-10 = 16
Amount spent on wife = 6+2*26
Amount spent on wife = 6+52
Amount spent on wife = $58
Hence, the amount spent on brother is $16, on sister is $26 and that on wife is $58.
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if f(x) has a remainder of -2 when divided by x-7, what is f(7)?
If f(x) has a remainder of -2 when divided by x-7, f(7) is -2.
The leftover is -2 when the function f(x) is divided by x-7, according to the question.
hence the result will be -2 if we use the value x = 7 in the function.
This has the same meaning as "f(7)" because "f(7)" also means to enter "x = 7" in the function and "-2" as the response.
Therefore, if f(x) is divided by x-7 with a remainder of 2, f(7) is equal to -2.
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On a cold day in new york, a street vendor sold 35 cups of hot chocolate and her entire stock of hot cider. if the ratio of cider to hot chocolate is 8:5, how many cups of cider did she sell?
Using the concept of ratio and proportion, the vendor sold 56 cups of hot cider.
How does a ratio operate?The word "proportion" often denotes a portion, share, or sum that is in comparison to a whole. Two ratios are in proportion when they are equal, according to the proportional idea. When an equation or a statement to that effect is used, two ratios or fractions are equal.
Define ratio.A percentage is a mathematical comparison of two numbers. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.
Cider supplied by the street seller for value = x for 35
= x/35
The cider's ratio is 8:5,
x/35 :: 8:5,
x = [35(8)]/ 5
=56.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 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 5.3 \text{ } (t > 0)[/tex]
50 points to the first person to answer this for me. Solve.
−2 1/3x=−1 3/4
What is the solution to the equation?
Enter your answer as a simplified fraction in the box.
Answer: [tex]x= \frac{3}{4}[/tex]
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
(2.92x10^6)/(4x10^-2)
Answer:
[tex]7.3 \times 10^7[/tex]
Step-by-step explanation:
[tex]\frac{2.92 \times 10^6}{4 \times 10^{-2}} \\ \\ =\frac{2.92 \times 10^8}{4} \\ \\ =0.73 \times 10^8 \\ \\ =7.3 \times 10^7[/tex]
-7t-8=10+2t solve for t
Answer:
t= -2
Step-by-step explanation:
Hope this helps!!
Answer:
t = -2
Step-by-step explanation:
-7t - 8 = 10 + 2t
Subtract 10 from both sides
-7t - 18 = 2t
Add 7t to both sides
-18 = 9t
Divide both sides by 9
-2 = t
You drove 18 miles in 20 minutes at a constant speed and did NOT exceed the speed limit, given in miles per hour. Among the following, which is the lowest that the speed limit could have been?
Answer:
54 mph
Step-by-step explanation:
18 miles / 20 minutes = 18 miles / 1/3 hour
18 ÷ 1/3 = 18 × 3 = 54 mph
The constant speed with given distance and time is 54 miles per hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, you drove 18 miles in 20 minutes at a constant speed.
Here, 20 minutes =20/60 =1/3 hours
Now, Speed = Distance÷Time
Speed= 18÷1/3
Speed=54 miles per hour
Therefore, the constant speed is 54 miles per hour.
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Find an equation for the line perpendicular to the line 4x - 9y = - 5 having the same y-intercept as - x - 4y = -2.
Clear y from both equations to find the slope y intercept form of the equations
[tex]\begin{gathered} 4x-9y=-5 \\ -9y=-4x-5 \\ y=\frac{-4x-5}{-9} \\ y=\frac{4}{9}x+\frac{5}{9}\text{ (Eq. 1)} \\ -x-4y=-2 \\ -4y=x-2 \\ y=\frac{x-2}{-4} \\ y=-\frac{x}{4}+\frac{1}{2}\text{ (Eq. 2)} \end{gathered}[/tex]Now, find the equation for the line that is perpendicular to Eq. 1 and has the same y intercept as Eq. 2
[tex]\begin{gathered} m1\cdot m3=-1 \\ m3=-\frac{1}{m1} \\ m3=-\frac{1}{\frac{4}{9}} \\ m3=-\frac{9}{4} \\ y=-\frac{9}{4}x+\frac{1}{2}\text{ (Eq. 3)} \end{gathered}[/tex]Eq. 3 is the equation for the line
MARY BOUGHT A CAR FOR $12,785 IF MARY PAID $2,000 DOWN AND WILL PAY $273.53 FOR 48 MONTHS WHAT IS THE TOTAL FINANCE CHARGE?
First, we will find the amount of money she will pay in 48 months
Since she pays $273.53 for 48 months, then
[tex]273.53x48=13,129.44[/tex]Since she paid a $2000 down payment
Then we will add 2000 to 13,129.44 to find the total amount she paid
[tex]T=13129.44+2000=15,129.44[/tex]Now, we will subtract the price of the car from it to find the finance charge
Since the price of the care is $12,785, then
[tex]\begin{gathered} T.F=15129.44-12785 \\ \\ T.F=2344.44 \end{gathered}[/tex]She will pay $2344.44 for the total finance charge
A dance club had 3 times as many members as an art club. the art club had 3,598 fewer members than the dance club. how many members did the art club have?
There are 1799 members in art club .
What is an linear equation ?A linear equation has the algebraic form y=mx+b, where m is the slope and b is the y-intercept, and consists of a first-order (linear) term and a constant. When x and y are the variables, the aforementioned is sometimes referred to as a "linear equation of two variables."
Each line in the Euclidean plane is conceived of as a collection of all the answers to a linear equation with two variables. Lines represent the solutions of linear equations in the Euclidean plane. This is where the word "linear," which is used to characterize this class of equations, originates.
Calculationd-dance club
a-art club
Lets set system of equations:
d=3a
a=d-3598
--------------
a=3a-3598
3598=3a-a
3598=2a
a=1799
so there are 1799 members in art club .
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Hi, I would like a step by step help on the blanks on how this problem was solved.-5 . (4 . 29) = (___ . ___) . 29= ____ . 29= -580
Recall that the distributive for the product property states that:
[tex]a*(b*c)=(a*b)*c.[/tex]Using the distributive property we get:
[tex]-5*(4*29)=(-5*4)*29.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} (-5*4)*29=-20*29 \\ =-580. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} -5*(4*29)=(-5*4)*29 \\ =-20*29 \\ =-580. \end{gathered}[/tex]
17. Is the following statement true or false? A triangle can have two angles that measure 100°.Explain.
the interior angles of the triangle must sum 180°
if we have two angles that measure 100° the sum of interior angles of a triangle will be more than 180°, and that can't be true.
so the answer is FALSE
Classify the system (options: consistent, independent consistent, inconsistent)3x + 2y = 73x - 4y = 9
SOLUTION
Let's look at the graphical solution of the pair of simultaneous equations
From the graph, we can see that the equations have at least one solution, which are 2.556, and -0.333. Hence, it is said to be consistent.
Now, since the solutions intersect only at one place, it means that it has exactly one solution. If a consistent equation has exactly one solution, it is said to be independent.
Therefore, the systems of equations are consistent and independent