The worth of the bond is $307.50.
What is the worth of the bond?The worth of the bond is the sum of the bond when it was bought and the interest earned on the bond.
Worth of the bond = interest rate + value when the bond was bought
Interest = 105% x $150
1.05 x $150 = $157.70
Worth of the bond = $157.70 + $150 = $307.50
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Given the above graph of y=-a(x+2)(x-6), where a>0,
(a) write down the equation of the line of symmetry,
(b) find the value of a.
Answer:
a)line x=2
b)a=3/2
Step-by-step explanation:
a) line of symmetry= x1 + x2/2=(-2)+6/2=2
b) (0,18)---y=-a(x+2)(x-6)
18=-a(0+2)(0-6)
a=18/12
a=3/2
Can someone help me?
square: 13² = 169 square units
rectangle: 15 x 8 = 120 square units
Coach Brown had to buy baseballs for his team. He bought practice baseballs at $1.75 each, rubber pitching machine balls at $2.80 each, and leather game balls at $6.25 each. He bought 250 balls in total, and 20 fewer game balls than pitching machine balls.
If the total came to $974.65, then how many of each ball were ordered?
A. 130 practice, 113 machine, and 93 game balls
B. 44 practice, 113 machine, and 93 game balls
C. 206 practice, 113 machine, and 93 game balls
D. 114 practice, 113 machine, and 73 game balls
44 practice, 113 machine, and 93 game balls
===========================================================
Explanation:
x = number of practice baseballsy = number of pitching machine baseballsz = number of game ballsHe bought 20 fewer game balls than pitching machine baseballs, which means,
z = y-20
Since the coach bought 250 baseballs total we can also write
x+y+z = 250
Let's replace z with y-20 and simplify
x+y+z = 250
x+y+y-20 = 250
x+2y = 250+20
x+2y = 270
Now let's calculate the subtotal costs for each type of baseball
1.75x = cost of just the practice baseballs2.80y = cost of just the pitching machine baseballs6.25z = cost of just the leather game balls.Those subtotals add to this
1.75x+2.80y+6.25z = total cost = $974.65
1.75x+2.80y+6.25z = 974.65
Like before, I'll replace z with y-20
1.75x+2.80y+6.25(y-20) = 974.65
1.75x+2.80y+6.25y-125 = 974.65
1.75x+9.05y = 974.65+125
1.75x+9.05y = 1099.65
------------------------------
So far we have this system of equations
[tex]\begin{cases}x+2y = 270\\1.75x+9.05y = 1099.65\end{cases}[/tex]
I'll use substitution to solve the system.
Isolate x in equation (1)
x+2y = 270
x = 270-2y
Then plug this into equation (2) and solve for y.
1.75x+9.05y = 1099.65
1.75(270-2y)+9.05y = 1099.65
472.5-3.5y+9.05y = 1099.65
472.5+5.55y = 1099.65
5.55y = 1099.65-472.5
5.55y = 627.15
y = 627.15/5.55
y = 113
There are 113 pitching machine baseballs.
Use this y value to find x
x = 270-2y
x = 270-2(113)
x = 270-226
x = 44
There are 44 practice baseballs.
Also, we can say,
z = y-20
z = 113-20
z = 93
There are 93 game balls.
------------------------------
Check:
x+y+z = 44+113+93 = 250 baseballs total
A = 1.75*x = 1.75*44 = 77 = cost of just the practice baseballsB = 2.80*y = 2.80*113 = 316.40 = cost of just the pitching machine baseballsC = 6.25*z = 6.25*93 = 581.25 = cost of just the game ballsA+B+C = 77+316.40+581.25 = 974.65 = total cost
Everything checks out. Also note that value of z is 20 fewer than the value of y.
in one week a farmer sells pumpkins to 60% of his customers. if 720 customers purchase pumpkins, how many total customers does the farmer have
A number is selected randomly from the integer from 10to30 what is the probability of picking a multiple of 4or5
Answer:
[tex]\frac{3}{7}[/tex]
Step-by-step explanation:
Start by finding how many integers there are from 10-30...
30-10+1=20+1=21
Note we have to add 1 since it is inclusive.
Now, let's find how many multiples of 4 or 5 there are from 10-30...
4*3=12
4*4=16
4*5=20
4*6=24
4*7=28
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5+5-1=9
Note we have to subtract 1 since 20 is counted twice.
The probability would be...
[tex]\frac{Multiples\ of\ four\ and\ five\ from\ 10-30}{Amount\ of\ integers\ between\ 10-30}=\frac{9}{21}=\frac{3}{7}[/tex]
Two friends, Justin and Andrew, had just bought their first cars. Justin uses 10 gallons of gas to drive 200 miles in his car. The table below represents the number of miles, yy, that Andrew can drive his car for every xx gallons of gas.
Answer:
andrew can drive 20 miles for every 1 gallon of gas
Step-by-step explanation:
please help asap !! (images below)
Answer:
5/4 and then 5/3
Step-by-step explanation:
Which angles are complementary to each other?
Answer:
All apply
Step-by-step explanation:
Complementary angles are ones that total 90°. Here, we have two pairs of congruent angles such that each pair totals 90°. We can mix and match to find pairs of complementary angles.
less than 45°: BGC and EGF
more than 45°: AGB and DGE
A complementary pair will consist of one angle from the first list and one angle from the second list. There are 4 possible pairings, and all are shown as answer choices.
All of the choices apply.
Which of the following best describes the graph below?
ļ ďd bd
5 4 3 2 1
1 2 3
4
&
-1
2.
2
-3
O A. It is not a function.
B. It is a many-to-one function.
C. It is a function, but it is not one-to-one.
D. It is a one-to-one function,
Answer: Most of the time, we're going to have to look at the graph of the function to determine its range. Examples. • Example 1 g(x) = 6x − 2. 3x − 4. (4).
5 pages
Step-by-step explanation:
hope this helps
The given graph is a one-to-one function
What is a function?A relation is a function if it has only One y-value for each x-value.
A function is said to be one-one if corresponding to each x we get a distinct y-value.
i.e. No two x have the same y-value.
Also it can be seen from the graph when any horizontal line is drawn parallel to the x-axis then the line intersect the curve atmost once.
it passes the horizontal line test.
Many-to-one function is a function is many to one when many x-values are mapped to same y-value.
Clearly from the graph we see that the graph is a one-to-one function.
Hence, the given graph is a one-to-one function
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The difference of a number and 13 is two less than the number doubled,
Three time
wal
quot
Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
13 - x = 2x - 2
or, 13 + 2 = 2x + x
or, 3x = 15
so, x = 5
5
When x = 0 and y = 0, which of the following is equivalent to
(5)?
Answer:
(b) x^15/y^5
Step-by-step explanation:
The exponent outside parentheses multiplies all of the exponents inside parentheses.
(x^3/y)^5 = x^(3·5)/y^(1·5) = x^15/y^5
______
Additional comment
When it comes to exponents, I find it useful to remember that an exponent signifies repeated multiplication: x·x·x = x³. The exponent outside parentheses has the same meaning:
(x³)² = (x·x·x)·(x·x·x) = x⁶
The rule is summarized by ...
(a^b)^c = a^(bc)
Question 6-89a
Find the perimeter of the figure below.
15 km
4 km
7 km
10 km
[tex]\\ \tt\hookrightarrow Perimeter [/tex]
[tex]\\ \tt\hookrightarrow 15+4+7+10[/tex]
[tex]\\ \tt\hookrightarrow 19+17[/tex]
[tex]\\ \tt\hookrightarrow 36km[/tex]
Find the area of the triangle
Step-by-step explanation:
total base length has to be found.
(√(3.6)^2+(3.25)^2+6.2)*3.25*.5=3.97
PLEASEEEE HELPPPPPPPPPP
this will provide you the answer
Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once.
View Available Hint(s)
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1. The slowly increasing distance between South America and Africa is due to _______.
2. Old Faithful Geyser at Yellowstone National Park in the United States acquires its energy from a ______.
3. Layered ______ exposed by erosion can be seen when looking at the Grand Canyon in the United States.
4. Australia is composed of relatively old and thick _________.
5. The extremely deep ocean Marianas Trench is a result of ______.
6. ______ found in the Atlantic Ocean between North America and Europe is composed of dense and relatively young rock.
7. The earthquakes that occur in Southern California generally occur above a ______.
a. Seafloor Spreading
b. Hot Spot
c. Sedimentary Rock
d. Continental Crust
e. Seafloor Crust
f. Fault
g. Fubduction
Seafloor spreading can be defined as a process that involves the formation of new oceanic crust as a result of volcanic activities and an upwelling of molten magma at mid-ocean ridges, as well as a slowly increasing distance (outward movement) from the ridge.
The theory of seafloor spreading was established by Harry Hammond Hess and it can be used to explain in details the slowly increasing distance between South America and Africa which grows from the center.
What is a hot spot?A hot spot refers to an area deep within Earth's mantle or under the rocky outermost layer of Earth, from which heat rises through convection and acquired as heat energy by a landform.
In the United States of America, you will see a layered sedimentary rock that is exposed by erosion when you view the Grand Canyon.
Furthermore, Australia is made up of relatively old and thick continental crust. Also, subduction causes the formation of extremely deep ocean Marianas Trench.
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Which of the following equations has both -5 and 5 as possible values of z?
z^2 =36
z^3 = 125
none of the above
The correct answer is z can take on the values of both -6 and 6, not -5 and 5.
The equation that has both -5 and 5 as possible values of z is:
[tex]z^2 = 36[/tex]
When we solve this equation, taking the square root of both sides, we get:
z = ±6
Therefore, z can take on the values of both -6 and 6, not -5 and 5.
Hence, none of the given equations have both -5 and 5 as possible values of z.For the equation z^2 = 36, we need to find the values of z that satisfy the equation. Taking the square root of both sides, we get:
z = ±√36
Simplifying the square root of 36, we have:
z = ±6
This means that z can take on the values of both -6 and 6. However, the values -5 and 5 are not solutions to this equation.
Similarly, for the equation z^3 = 125, there are no values of z that satisfy the equation for z equal to -5 or 5.
Therefore, none of the given equations, z^2 = 36 and z^3 = 125, have both -5 and 5 as possible values of z.
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What is the original polynomial
Step-by-step explanation:
We know that divisor = (dividend)(quotient)+remainder.
So we can do (x^2 - x +8)(x+4)-5, which you can just expand out.
which equation has the solution x=7?
2x+5=19
5x-2=-33
4x-9=13
7x+5=96
[tex]2x + 5 = 19 \\ 2 \times 7 + 5 = 19 \\ 14 + 5 = 19 \\ 19 = 19 [/tex]
So, The first equation has the solution x = 7
Suppose 700 students were surveyed. How many more students prefer music over social
studies?
Given m is parallel to n, find the value of x???
Answer:
x = 62
Step-by-step explanation:
The angle adjacent to 118° is
180° - 118° = 62°
x and 62 are corresponding angles and are congruent , so
x = 62
easy math problem !,!!,!
A- 9B- 87C- -2D -9
Step-by-step explanation:
The data set represents a progression of hourly temperature measurements. Use a graphing calculator to determine the quadratic regression equation for this data set. X 0 1 2 3 4 5 y 20 16 10 0 -7 -20 a. Y = 0. 795 x squared 3. 796 x 20. 180 c. Y = negative 0. 875 x squared minus 3. 596 x 20. 179 b. Y = negative 0. 795 x squared minus 3. 760 x 20. 180 d. Y = negative 0. 795 x squared minus 3. 796 x 20. 180.
A regression can be modeled by linear regression, quadratic regression, quartic regression or exponential regression
The quadratic regression equation that models the data is
[tex]\^y = -0.875\^x^2 -3.596\^x +20.179[/tex]
How to determine the regression equationThe table entries are given as:
x: 0,1,2,3,4,5
y: 20,16,10,0,-7,-20
A quadratic regression is represented as:
[tex]\^y = a\^x^2 + b\^x + c[/tex]
Using a graphing calculator to determine the quadratic regression equation, we have the following calculation summary
a = -0.875
b = -3.596
c = 20.179
Hence, the quadratic regression equation is:
[tex]\^y = -0.875\^x^2 -3.596\^x +20.179[/tex]
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Answer:
ITS C
Step-by-step explanation:
A video game costs $16.40 before tax. What is the total cost after the 5% sales tax?
Answer:
$17.22
Step-by-step explanation:
→ Find the multiplier
( 100 + 5 ) ÷ 100 = 1.05
→ Multiply answer by cost
16.40 × 1.05 = $17.22
What is the solution of the equation
Answer: x=-56/3 (the second answer)
what’s the slope?
50 points!! Please help
Answer:
6
Step-by-step explanation:
slope is rise/run
to get from -1 to 5 is 6 points
y axis to 1 is 1 point
6/1=6
Multiply
5 ft x 9 ft = __
what is
x - 2 5/8 = 6 1/4
Answer:
x = 8 7/8
Step-by-step explanation:
x + -21/8=25/4
+ 21/8 +21/8
x = 71/8
x = 8 7/8
PLSSS SOMEONE HELP ME FASTt
Answer:
50%
Step-by-step explanation:
29/58 = 0.5
0.5 = 50%
The function f(x) = -(x+4)^2+5 is written in vertex form and shows that the vertex of the graph of f is located at (-4,5)
Each value of the f can be obtained from two different x-values except f(x)=5. Which best explains why f(x)=5 is the output for only one input value?
There is only one value for x that makes [tex](x+4)^2=0[/tex]
Vertex form of an expressionGiven the vertex form of the function expressed as:
[tex]f(x) = -(x+4)^2+5[/tex]
If the function f(x) = 5
[tex]5 = -(x+4)^2+5[/tex]
Subtract 5 from both sides
[tex]5 = -(x+4)^2+5\\-(x+4)^2= 5-5\\-(x+4)^2=0\\[/tex]
Hence there is only one value for x that makes [tex](x+4)^2=0[/tex]
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I need help asap this is due the next day
7. the graphed solution (bold line) shows inequalities x≥-1
this is the same as inequality: x + 1 ≥ 0 (A)