Let the length of one leg be x, then other leg length is (x+2).
Determine the length of leg of triangle by using the pythagoras theorem.
[tex]\begin{gathered} (10)^2=(x)^2+(x+2)^2 \\ 100=x^2+x^2+4x+4 \\ x^2+2x-48=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x+8)=0 \\ (x-6)(x+8)=0 \end{gathered}[/tex]So values of x is 6 and -8. Negative length is not possible. The value of x is 6.
Determine the length of other leg.
[tex]\begin{gathered} x+2=6+2 \\ =8 \end{gathered}[/tex]Thus length of legs of triangle are 6 ft and 8 ft.
Solve the system using substitution. You can eliminate the decimals if you like, but you don’t have to. The solution will be the same in either case. {0.45x + 0.10y = 4.30 y = 22-x (x,y)= (_, _)
SOLUTION:
Case: System of equations
Method:
[tex]\begin{gathered} 0.45x+0.10y=4.30....(1) \\ y=22-x....(2) \\ Substitute\text{ }y=22-x\text{ }into\text{ }eqn(1) \\ 0.45x+0.10y=4.30 \\ 0.45x+0.10(22-x)=4.30. \\ 0.45x+2.2-0.1x=4.30 \\ 0.45x-0.1x=4.3-2.2 \\ 0.35x=2.1 \\ x=\frac{2.1}{0.35} \\ x=\frac{210}{35} \\ x=6 \end{gathered}[/tex]Put x = 6 in y= 22 -x
[tex]\begin{gathered} y=22-x \\ y=22-6 \\ y=16 \end{gathered}[/tex]Final answer:
(x,y) = (6, 16)
how do you write 7,500,000,000,000,000,000 in scientific notation
7,500,000,000,000,000,000
In scientific notation, the 10 raised to a power having put the number to standard form
7,500,000,000,000,000,000
= 7.5 * 10^18
A line is drawn on a coordinate plane so that it is parallel to the x-axis and passes through the point (4.6). Which statement identifies equation and slope of this line?
A. The equation of the line is y = 6, and the slope is 0
Explanations:Note that:
When a line is parallel to the x -axis, the slope of that line equals to zero
According to the question, the line passes through the point with coordinates (4, 6)
The equation of a line passing through a point of coordinates (x₁ , y₁) is given by the equation:
y - y₁ = m ( x - x₁)
x₁ = 4, y₁ = 6
Substitute x₁ = 4, and y₁ = 6 into the given equation:
y - 6 = 0(x - 4)
y - 6 = 0
y = 6
The equation of the line is y = 6, and the slope is 0
I need help with this practice I believe the subject for this is complex numbers and vectors I will send you an additional picture that goes along with this, it is a graph, use the graph to answer
Solution
- In order to plot these vectors using Parallelogram law, we need to write them in rectangular form i.e. in terms of the x and y-components.
- This is done below:
[tex]\begin{gathered} \vec{a}=-3i-5j \\ \vec{b}=i+4j \end{gathered}[/tex]- We can then proceed to plot the vectors on a graph.
- For vector a, the line of magnitude extends from the origin (0, 0) to the point (-3, -5) while the line of the magnitude of vector b extends from the origin (0, 0) to the point (1, 4).
- This is shown below:
- The vector addition of both vectors is given below:
[tex]\begin{gathered} \vec{a}+\vec{b}=-3i-5j+(i+4j) \\ \text{ Add only magnitudes of the same component} \\ \vec{a}+\vec{b}=-3i+i-5j+4j \\ \\ \therefore\vec{a}+\vec{b}=-2i-j \end{gathered}[/tex]- This implies that the vector addition of both vectors extends from the origin (0,0) to the point (-2, -1)
- This is depicted below:
Wesley Snipes ears a monthly salary of $1,685, plus a 8.5% commission on all sales over $2,000 each month. This month, his sales were $6,250. What was his totalincome for the month?$2,224.50$2,175.80$2,112.90$2,046.25None of these choices are correct.
His total income for the month is $2,216.25 and that means none of these choices are correct
Here, we want to get the total income for the month
Now, what we have to add to the monthly salary is the commission percentage amount
From the question, this is simply 8.5% of $6,250
Thus, we have it that;
[tex]\frac{8.5}{100}\times\text{ 6,250 = \$531.25}[/tex]We now proceed to add this to the salary
We have the total as;
[tex]1,685\text{ + 531.25 = \$2,216.25}[/tex]MVT of a function x^2-6x+8 on (0,8)
According to the Mean Value Theorem:
[tex]f^{\prime}(c)\text{ = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex][tex]f^{\prime}(c)\text{ = }\frac{f(8)-f(0)}{8-0}[/tex]f(x) = x² - 6x + 8
f(0) = 0² - 6(0) + 8
f(0) = 8
f(8) = 8² - 6(8) + 8
f(8) = 64 - 48 + 8
f(8) = 24
f'(x) = 2x - 6
f'(c) = 2c - 6
[tex]\begin{gathered} 2c\text{ - 6 = }\frac{24-8}{8} \\ 2c\text{ - 6 = }\frac{16}{8} \\ 2c\text{ - 6 = 2} \\ 2c\text{ = 2 + 6} \\ 2c\text{ = 8} \\ c\text{ = }\frac{8}{2} \\ c\text{ = 4} \end{gathered}[/tex]State if the two triangles are congruent and by what thermoe
Although the triangles seems right triangles, we can't assume it because they might be out of scale.
So, the informations we have are:
They have a side wity equal length followed by a common side, thus it also has common length, and followed by an angle with common measure.
This is a case of Side-Side-Angle, and this is not enough to prove congruency.
So, the answer is that, we can't confirm if they are congruent or not.
1 of 9Place and label the following numbers on the number line.175-1.75Line Reader help me .
Ok, so:
We're going to place and label the following numbers on the number line.
-1
1.75
-1.75
-2
-2 1/2 = -3/2
-5/2
9/4
Sketch a system of two linear equations whose solution is (-1, 3).T
The two system of equations
y = 2x + 3
and
y = -3x has a solution ( -1, 3 )
My I please get help with this math. I need help answering for each of them
Find a formula for the nth termof the arithmetic sequence.First term 9Common difference -2an = [? ]n + []
Given:
First term 9
Common difference -2
Required:
Find a formula for the nth term of the arithmetic sequence.
Explanation:
The general formula for the nth term of the an arithmetic sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]Where a = first term
d = common difference
Put a = 9 and d = -2 in the formula.
[tex]\begin{gathered} a_n=9+(n-1)(-2) \\ a_n=9-2(n-1) \\ a_n=9-2n+2 \\ a_n=-2n+11 \end{gathered}[/tex]Final Answer:
The nth term of the arithmetic sequence is
[tex]a_n=-2n+11[/tex]You have a line AB where A is (0,3) and B is (2,7) find a point P that partitions the line 1:2.
ANSWER:
[tex]P=(\frac{2}{3},\frac{13}{3})[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula to calculate the point P
[tex]\begin{gathered} x_p=\frac{x_2\cdot a+x_1\cdot b}{a+b}_{} \\ y_p=\frac{y_2\cdot a+y_1\cdot b}{a+b}_{} \\ a\colon b=1\colon2 \\ (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,7) \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} x_p=\frac{2\cdot1+0\cdot2}{1+2}=\frac{2+0}{3}=\frac{2}{3} \\ y_p=\frac{7\cdot1+3\cdot2}{1+2}=\frac{7+6}{3}=\frac{13}{3} \\ \text{The point p is:} \\ (\frac{2}{3},\frac{13}{3}) \end{gathered}[/tex]Lindan just received a dozen roses for her birthday. For the flowers, she fills up a rectangular vase with water. The vase has a square bottom that is 3 inches in width. The base stands 12 inches tall. There is a sponge filling the bottom of the vase for the flower stands. It is 4 inches tall. How much space is left in the vase with for flowers?
Volume of the vase = 3 x 3 x 12 = 108 in^2
Volume of the sponge = 3 x 3 x 4 = 36 in^2
Volume left = 108 - 36 = 72 in^2
Multiply and simplify completely: (4p + 2)(6p - 3) Show all work
(4p + 2)(6p - 3) = 4p(6p - 3) + 2(6p -3) = 24p^2 - 12p + 12p -6 = 24p^2 - 6 = 6(4p^2 -1)
[tex](4p\text{ + 2)(6p-3) = 4p(6p-3) + 2(6p-3) = }24p^2-12p+12p-6=24p^2-6=6(4p^2-1)[/tex]Answer:
[tex]6(4p^2-1)[/tex]How do I find the measurement of b? Is the correct answer 52 degrees
Remember that
An isosceles triangle has two equal sides and two equal interior angles
so
In this problem
Triangle ABC is an isosceles triangle
because
AB=BC ----> given
that means
mso
y=52 degrees
The sum of the interior angles in any triangle must be equal to 180 degrees
so
msubstitute given values
52+m
solve for m
mm
1. Problem Set B: For each of the following problems, include a sketch of the scenario, name the characteristic the question is asking for and how you will solve for that characteristic. An object is dropped from a bridge over a bay. Its motion is modeled by the quadratic equation h(t) = -16t^2 +56 where t represents the time since the object was dropped and h(t) represents the height of the object. a. How long will it take for the object to reach the water?b. How will you find this characteristic?c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56? a. It takes 56 seconds for the object to reach the ground. b. The object is 56 feet above the ground initially. c. The object reaches its maximum height after 56 seconds.
we have the equation
h(t) = -16t^2 +56
Part a. How long will it take for the object to reach the water?
when the object reach teh water h(t)=0
so
For h(t)=0
solve for t
0=-16t^2+56
16t^2=56
t^2=56/16
t^2=3.5
t=(+/-)1.87
therefore
answer part a is t=1.87 secRemember that the time can not be negative
Part b. How will you find this characteristic?
because if the object reach the water is when the height is zero (sea level is the zero)Part c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56?
answer is
b. The object is 56 feet above the ground initially.What is the value of(-* - ) =( 4 )?-1516-516
Answer
Option B is correct.
[tex]-1\frac{5}{16}[/tex]Explanation
To answer this, we will first deal with the value in the first bracket by taking LCM
[tex]\begin{gathered} (-\frac{1}{4}-\frac{1}{2}) \\ =\frac{-1-2}{4} \\ =\frac{-3}{4} \end{gathered}[/tex]Then to solve the part with division, we know that the division involving fractions are solved by changing the division sign into multiplication sign and the fraction after the sign changes to its reciprocal or its inverse.
[tex]\begin{gathered} (-\frac{3}{4})\div\frac{4}{7} \\ =-\frac{3}{4}\times\frac{7}{4} \\ =-\frac{21}{16} \\ =-1\frac{5}{16} \end{gathered}[/tex]Hope this Helps!!!
A bottlenose dolphin is 10 feet belo sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation,y, after x seconds
x + 3 = y, make x the subject of the formula 1. x = y + 3 2. x = 3y3. x = y-3 4. x=y/3PLEASE HELP ME
Make x the subject of the formula
x + 3 = y
This means you re-write the equation such that x woukd be on one side of the equation alone (usually the left side) and all other terms would be on the other side of the "equal to" sign.
[tex]\begin{gathered} x+3=y \\ \text{Subtract 3 from both sides} \\ x+3-3=y-3 \\ x+0=y-3 \\ x=y-3 \end{gathered}[/tex]The answer is x = y - 3
=Find the variance for the set of data: 26, 34, 17, 24, 24.The variance is0.
The variance is:
[tex]\sigma^2=\frac{\Sigma(x-\mu)^2}{N}[/tex]So we have 5 values, which means that N=5 and the mean is:
[tex]\mu=\frac{26+34+17+24+24}{5}=25[/tex]So the variance is 29.6.
5. If the area of a parallelogram is 456 cm2 and the base is 24 cm. Find the height. Height = 1.
The area of a parallelogram is computed as follows:
A = base*height
Substituting with A = 456, and base = 24,
456 = 24*height
456/24 = height
19 cm = height
#(13) Admission to the fair costs $7.75. Each ride costs you $0.50. You have $15 to spend at the fair including admission. Wrtie an inequality to best model this situation. Using the inequality that you chose in #13 what is the maximum number of rides you can go on?
We have the next information
7.75 admission
0.50 ride
you have 15 that is the limit
The inequality will be
[tex]7.75+0.50x\le\text{ 15}[/tex]where x is the number of rides you can do
Using the inequality we can calculate the number of rides, we need to clear x
[tex]\begin{gathered} 0.50x\le15-7.75 \\ 0.50x\le7.25 \\ x\le\frac{7.25}{0.50} \\ x\le14.5 \end{gathered}[/tex]the maximum number of rides is 14 because we can't do a half ride
Factor this question Q3+125
write 125 as a power in base 5
[tex]q^3+5^3[/tex]then, apply the rule for the addition of cubes
[tex]\begin{gathered} a^3+b^3=(a+b)\cdot(a^2-a\cdot b+b^2) \\ \text{then, } \\ q^3+5^3=(q+5)\cdot(q^2-5x+5^2) \\ q^3+5^3=(q+5)\cdot(q^2-5x+25) \end{gathered}[/tex]Express your answer as a polynomial in standard form.9f(x) = x2 - 4x –g(x) = -3x – 5Find: f(g(x))
Given the functions:
[tex]\begin{gathered} f(x)=x^2-4x-9 \\ g(x)=-3x-5 \end{gathered}[/tex]We need to find the function f(g(x)
So, every variable for x in the function f(x) will be substituted with g(x) as follows:
[tex]f(g(x))=(-3x-5)^2-4\cdot(-3x-5)-9[/tex]Now, we will simplify the expression:
[tex]\begin{gathered} f(g(x))=9x^2+30x+25+12x+20+9 \\ \\ f(g(x))=9x^2+42x+54 \end{gathered}[/tex]So, the answer will be:
[tex]f(g(x))=9x^2+42x+54[/tex]Select ALL the true statements1 poClare created Figure A Then she created Figure B by translating Triangle C and thentranslating Triangle D.Figure AFigureсDFigure A is congruent to Figure BFigure B is a translation of Figure A.Triangle Cis congruent to Triangle CTriangle D'is congruent to Triangle D.
The first statement cannot be true since the complete figure is not the same and sides cannot be overlapped together and look the same without a translation.
The second statement is not true either because if the full figure was translated it would look the same in another position and this is not the case.
The third and forth statements are true because figures were translated and didn't suffer any expansions or contractions which means that all of its sides must be equal and make them congruent.
Jessica is the secretary of the Hillside Players.They are going to put on a show at the village hall.Jessica needs to arrange 4dates in October for rehearsals
ANSWER :
EXPLANATION :
a
As part of a class project, a university student surveyed students in the cafeteria to look for a relationship between the students' eye color and hair color. The table contains the survey results. Match the descriptions with the correct values.
Ok, so
If we analyze the tab, we notice the following things:
- The number of students with blue eyes and blond hair is 42. That's because if we go to the table and look at the rows and columns, 42 is the number which relations these two facts.
- The number of students with gray eyes and brown hair, is 5. That's because if we go to the table and look at the rows and columns, 5 is the number which relations these two facts.
- The difference of the number of students with gray eyes and brown hair and the number of students with green eyes and black hair is:
- Green eyes and black hair - gray eyes and brown hair
=> 11 - 5, which is 6.
slope is ___ of change in a relationship.
The slope is the rate of change of 2 variables associated.
Usually the rate of change of y with x.
But it can be of any 2 variables in the problem.
So, the slope is the rate.
The rate at which something is changing with respect to another thing.
Thus,
Answer:
slope is rate of change in a relationship.
If one zero of 5² + 13 + is the reciprocal of the other, find the value of k?
Answer:
k = 5
Explanation:
The given polynomial is
5² + 13 +
Let one of the zeros be z. Given that one of the zero is the reciprocal of the other, the reciprocal of z is 1/z. The roots are z and 1/z
The standard form of a quadratic polynomial is
ax^2 + bx + c
By comparing the polynomial expressions,
a = 5, b = 13, c = k
The product of the roots of a quadratic polynomial is c/a = k/5
Thus,
1/z * z = k/5
1 = k/5
By cross multiplying,
k = 5
I have this question and I can’t figure it out
SOLUTION:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Therefore from the question, the integers are:
[tex]-2,-1,0,2[/tex]The number line is shown below