The future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
Given that business person invests $3,367 at 5% compounded semiannually for two years.
p = $3,367
r = 5%
t = 2 years
A = P(1+r/100)ⁿ
Substitute the values of p,r, and t in the formula,
A = 3,367(1 + 5/100)²
A = 3,367(1 + 0.05)²
A = 4.700 (1.05)²
A = 3712.1175
Rounded to the nearest cent
A = $3712.1
Total interest = A - p = 3712.1 - 3,367 = $345.1
Therefore, the future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
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i need to know what box i drag each , i tried to attach all them but it didnt allow me .
Triangle ABC has two angles measuring 59º and 88º. The third angle can be found by using the fact that the three angles of a triangle must sum up to 180º.
So, we have:
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \\ 88^{\circ}+\angle B+59^{\circ}=180^{\circ} \\ \\ 147^{\circ}+\angle B=180^{\circ} \\ \\ \angle B=180^{\circ}-147^{\circ} \\ \\ \angle B=33^{\circ} \end{gathered}[/tex]Now we know the measures of all angles and sides of the given triangle, let's analyze each of the congruence cases.
• For, triangle DEF, we see that:
Side DE is congruent to side AB (because they are represented using the same symbol)
Side EF is congruent to side BC (again, they both are represented by the same symbol)
The angle between sides DE and EF is congruent to the angle between sides AB and BC (they both measure 33º).
Thus, triangle DEF has a pair of sides, and the angle between them congruent two a pair of sides and the angle between them of triangle ABC.
Therefore, those two triangles are congruent by the Side-Angle-Side theorem. Or, for short: SAS.
• For ,triangle GHI ,we see that:
It has a pair of angles, 33º and 59º, that are congruent to a pair of angles of triangle ABC. Also, the side HI between those angles is congruent to side BC.
Thus, triangle GHI and triangle ABC are congruent by the Angle-Side-Angle Theorem. Or, for short: ASA.
For triangle
1.2.12 m18 inC3.4.35 km5.6.15.6 cm7 mm
The required solution is the circumference of the circle for the given radius or diameter
The formula for the circumference of a circle with radius r is :
[tex]C\text{ = 2 }\pi\text{ r}[/tex]The formula for the circumference of a circle with diameter d is:
[tex]C\text{ = }\pi\text{ d}[/tex]For the first circle with a radius of 12m:
[tex]\text{Circumference = 2}\times\text{ }\pi\text{ }\times\text{ 12 = 24}\pi[/tex]For the second circle with a diameter of 18in :
[tex]C\text{ = }\pi\text{ }\times\text{ 18 = 18}\pi[/tex]For the third circle with a radius of 2.8ft:
[tex]\begin{gathered} C\text{ = 2 }\times\text{ }\pi\times\text{ 2.8 } \\ =\text{ 5.6}\pi \end{gathered}[/tex]For the fourth circle with a diameter of 35km:
[tex]\begin{gathered} C\text{ = }\pi\text{ d} \\ =\text{ }\pi\text{ }\times\text{ 35 = 35}\pi \end{gathered}[/tex]For the fifth circle with a radius of 7mm:
[tex]\begin{gathered} C\text{ = 2 }\times\pi\times\text{ r} \\ =\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 7} \\ =\text{ 14}\pi \end{gathered}[/tex]For the sixth circle with a radius of 15.6 cm:
[tex]\begin{gathered} C\text{ = 2}\pi r \\ =\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 15.6 } \\ =\text{ 31.2 }\pi \end{gathered}[/tex]Note: Circumference has a unit. It's unit depends on the unit of the radius/ diameter
What is the standard deviation of the data?Some teenagers collected trash for a beach cleanup.The data for the number of pounds of trash collected byeach teenager are shown below.26, 26, 21, 22, 20, 25, 35O pounds4.66 pounds5.03 poundso 25.33 pounds
the average age of a family of 6 is 30 years. the average of the 3 children in the family is 12 years. if the mother is 4 years younger than the father , calculate the age of the father
In order to calculate the age of the father, you first consider that the average of the family is 30, then, you have:
(x1 + x2 + x3 + x4 + x5 + x6)/6 = 30
where x3, x4, x5 and x6 are the ages of the children, x1 is the age of the mother and x2 is the age of the father
You cn write the previous expression as:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
The second term in the second expression is the average age of the children, which is 12. Furthermore, the mother is 4 years younger than the father, that is, x1 = x2 - 4. You replace this values in the expression above and you obtain:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
(x2 - 4 + x2)/7 + 12 = 30
Next, you solve for x2:
(x2 - 4 + x2)/7 + 12 = 30
(2x2 - 4)/7 + 12 = 30
multiply the previous expression by 7:
2x2 - 4 + 12(7) = 30(7)
2x2 - 4 + 84 = 210
2x2 = 130
x2 = 65
Then, the age of the father is 65
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Which postulate or theorem could you use to prove AXYZ AABC?
Choose the correct answer below.
O SSS postulate
OSAS postulate
O ASA postulate
O AAS theorem
2.90change repeating decimal to fraction?
The given number is 2.90.
As you can notice this is a decimal number which is also rational. To express as a fraction, we divide it by 100 to get rid of the decimal point, then we simplify, as follows
[tex]\frac{290}{100}=\frac{145}{50}=\frac{29}{10}[/tex]Therefore, the equivalent fraction is 29/10.c and 217 more is equal to 198
c and 217 more means c+217
equal to 198 means =198
the complete sentence means
c+217=198
Suppose that $6500 is placed in an account that pays 3% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.
Given
Part A
[tex]\begin{gathered} P=\text{ \$6,500} \\ r=3\text{ \%} \\ t=1 \end{gathered}[/tex]Formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=6,500(1+\frac{0.03}{1})^{1\times1} \\ \\ A=6,500(1.03) \\ A=\text{ \$}6,695 \end{gathered}[/tex]Part B
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ P=6500 \\ R=3\text{ \%} \\ t=2 \end{gathered}[/tex][tex]\begin{gathered} A=6500(1+\frac{0.03}{1})^{1\times2} \\ \\ A=6500(1.03)^2 \\ A=6500(1.0609) \\ A=\text{ \$}6895.85 \end{gathered}[/tex]The final answer
DAC BAD.What is the length of BD?Round to one decimal place.
Notice that we have two triangles with the SAME angle, abd with also a common side (the same length) AD.
we can use the law os sines in the smaller triangle and specially using the sides that are known.
for example, we can state in the first (smaller) triangle that:
[tex]\frac{\sin(\theta)}{2}=\frac{\sin (D)}{5.9}=\text{ }\frac{\sin(C)}{AD}[/tex]For the full triangle ABC we have the following law of sines:
[tex]\frac{\sin(2\theta)}{2+\text{?}}=\text{ }\frac{\sin(C)}{8.1}=\frac{\sin (B)}{5.9}[/tex]For the medium triangle ADB the law of sines goes as:
[tex]\frac{\sin(\theta)}{?}=\frac{\sin(B)}{AD}=\frac{\sin(180-D^{})}{8.1}=\frac{\sin (D)}{8.1}[/tex]Now, we need to find common variables to combine equations based on the law of sines.
Notice as well that sin(180-a) = sin(a) this is a trig identity, so we are going to replace this in the last trig identity for triangle ADB
Now, we have the following relationships from the veri first law of sines:
[tex]\sin (\theta)=\frac{2\cdot\sin (D)}{5.9}[/tex]and from the last law of sines we have the folloowing relationship:
[tex]\sin (\theta)=\frac{?\cdot\sin (D)}{8.1}[/tex]so we can equal both sine expressions since they are from the same angle, and try to solve for the unknown "?" in the equation:
[tex]\begin{gathered} \frac{2\cdot\sin(D)}{5.9}=\frac{?\cdot\sin (D)}{8.1} \\ \frac{2}{5.9}=\frac{?}{8.1} \\ \frac{2\cdot8.1}{5.9}=\text{?} \end{gathered}[/tex]whre we have eliminated sin(D) as common factor in both equations (this is correct as long as sin*D) is not equal to zero, which cleary is not the case here)
Therefore our unknown "?" is 2*8.1 / 5.9 = 2.7457 which rounded to one decimal is 2.7
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.3%. If the enrollment in associatedegree programs in 2014-2015 is 7,800,000, find the increase and the projected number of students in an associate degree program in 2024-2025.The increase is(Round to the nearest whole number as needed.)The projected number of students in an associate degree program in 2024-2025 is(Round to the nearest whole number as needed)
First, let's convert the percentage into a decimal:
[tex]\frac{21.3}{100}\rightarrow0.213[/tex]And multiply it by the initial amount:
[tex]7800000\cdot0.213=1661400[/tex]This way, the increase would be 1,661,400 , and the proyected number of students would be 9,461,400
A. graph quadrilateral KLMN with vertices K(-3,2),L(2,2),M(0,-3)and N(-4,0) on the coordinate grid.B. on the same coordinate grid,graph the image of quadrilateral KLMN after a translation of three units to the right and four units up.C. witch side of the image is congruent to side LM?Name three other pairs of congruent sides.
The given points are K(-3,2), L(2,2), M(0,-3), and N(-4,0).
If we graph part A, it would be as the image below shows
Notice that these four points for a quadrilateral.
Now, part B is about shifting the quadrilateral three units right and four units up, so its new coordinates would be K'(0,6), L'(5,6), M'(3,1), and N'(-1,4). So, the new parallelogram is shown in the image below, where you would notice the pre-image and the image.
According to the image above, side LM is congruent to L'M', they are corresponding sides of the transformation. The other three congruent sides are NK to N'K', MN to M'N', and KL to K'L'.
at Mr.neelys farm, there were 75 sheep and 60 cows what is the ratio number of cows to the number of sheep's at Mr.neelys farm
Answer:
The ratio of the number of cows to the number of sheeps in the farm is;
[tex]\begin{gathered} \frac{4}{5} \\ Or \\ 4\colon5 \end{gathered}[/tex]Explanation:
Given that;
there were 75 sheep
and 60 cows
We want to find the ratio of the number of cows to the number of sheeps in the farm;
[tex]\text{ratio}=\frac{\text{ number of cows }}{\text{ number of sh}eeps}=\frac{60}{75}[/tex]reducing the ratio to the least form;
[tex]\text{ratio=}\frac{60}{75}=\frac{4}{5}[/tex]Therefore, the ratio of the number of cows to the number of sheeps in the farm is;
[tex]\begin{gathered} \frac{4}{5} \\ Or \\ 4\colon5 \end{gathered}[/tex]"The sum of 5 and a number results in 14."
We are given the phrase "The sum of 5 and a number results in 14." which suggest that we should find such a number. Let x be the number we are looking for, the phrase "The sum of 5 and a number" translates to the equation x+5,, since we are adding 5 to the number.
The part "results in 14" means that after adding 5, we end up having 14 as a result, this means we have
[tex]x+5=14[/tex]Now, we proceed to solve this equation for x by simply subtracting 5 on both sides. Once we do so, we get
[tex]x=14-5=9[/tex]so in this case the number we were looking for is x=9.
if the spinner was fair and spun 300 times,each outcome would be expected to be observed_____times.
ANSWER
Each outcome would be expected to be observed 75 times.
EXPLANATION
We have to find the theoretical probability of each outcome. If the spinner is fair, each outcome is equally probable. If we were to spin it 300 times, and the spinner has 4 sections, we would expect that each outcome to be observed:
[tex]\frac{300}{4}=75[/tex]75 times each section.
Find the product: (2×^2+3)^2
(2x + 3)²
We will simply expand
(2x + 3)(2x + 3)
2x(2x+3) + 3(2x+ 3)
open the parentheses
4x² + 6x + 6x + 9
4x² + 12x + 9
Х о 1 2 3 4 у -5 4 13 22 31
We can take any 2 points both from x and y and use the equation of a line formula to find out the equation of the line represented by the points in the table.
Let's take the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]The equation of a line formula is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us plug in the points into this formula and do a little algebra to re-arrange the equation in the slope-intercept form, which is y = mx + b. The steps are shown below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-5)=\frac{4-(-5)}{1-0}(x-0) \\ y+5=\frac{4+5}{1}(x) \\ y+5=\frac{9}{1}(x) \\ y+5=9x \\ y=9x-5 \end{gathered}[/tex]The slope-intercept form is given by:
[tex]y=9x-5[/tex]Where 9 is the slope and -5 is the y-intercept (y-axis cutting point)
Hello! I'm having a hard time solving and graphing this
Answer:
A = 25π units² = 78.5 units²
Explanation:
The circle with a center at (-1, 2) that passes through (-6, 2) has a radius equal to 5 because the distance between the center and the point is calculated as
-1 - (-6) = -1 + 6 = 5
Then, the area of the circle is equal to
A = πr²
A = π(5)²
A = 25π
Replacing π = 3.14, we get
A = 25(3.14)
A = 78.5
Therefore, the answer is
A = 25π units² = 78.5 units²
Line c passes through the points (3, - 5) and (6, 1) . Line d passes through the points (6, - 4) and (2, - 2) Find the slope of each line and determine whether lines c and d are parallel , perpendicular , or neither . Explain your answer ...
Answer:
The slope of line c is 2.
The slope of line d is -1/2.
Lines c and d are perpendicular
Step-by-step explanation:
Slope of a line:
When given two points of a line, the slope is given by the change in y divided by the change in x.
Parallel lines: Have the same slope
Perpendicular lines: The multiplication of their slopes is -1.
Line c:
Passes through points (3,-5) and (6,1).
Change in y: 1 - (-5) = 1 + 5 = 6
Change in x: 6 - 3 = 3
Slope: 6/3 = 2
The slope of line c is 2.
Line d:
Passes through points (6,-4) and (2,-2)
Change in y: -2 - (-4) = -2 + 4 = 2
Change in x: 2 - 6 = -4
Slope: 2/-4 = -1/2
The slope of line d is -1/2.
Relationship between the lines:
They have different slopes, so they are not parallel.
Multiplication of the slopes:
2*(-1/2) = -2/2 = -1
Since the multiplication of their slopes is -1, Lines c and d are perpendicular.
Which of the following is equivalent to the radical expression below when x is greater than or equal to 7
SOLUTION
The radical expression given is
[tex]\sqrt[]{x-7}.\sqrt[]{x+1}[/tex]Applying the rule
[tex]\sqrt[]{a}\times\sqrt[]{b}=\sqrt[]{ab}[/tex]We obtain
[tex]\sqrt[]{x-7}\times\sqrt[]{x+1}=\sqrt[]{(x-7)(x+1)}[/tex]Expanding the parenthesis, we have
[tex]\begin{gathered} \sqrt[]{(x(x+1)-7(x+1)} \\ =\sqrt[]{x^2+x-7x-7} \\ =\sqrt[]{x^2-6x-7} \end{gathered}[/tex]The radical expression is equivalent to
[tex]\sqrt[]{x^2-6x-7}[/tex]The right option is A
Pablo draws Rectangle P. He says that the area is greater than 50 square units. What could the missing side length be? Explain. P. ? units 6 units
Answer:
Explanation:
Here, we want to get the missing side length
From the question, it was said that the area is greater than 50 square units
What this mean is that the product of the width and length of the rectangle is greater than 50 square units
Therefore, the number in whch we will multiply by 6 must give us a result greater than 50 square units
The highest multiple of 6 closest to 50 is 48 while the closest multiple after 50 is 54
9 multiplied by 6 will give 54 square units
In essence, we can say that the missing side length is 9 square units
Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x² + 4x - 5. If there is more than one x-Intercept, separate them with commas.DD:x-intercept(s):5?vertex:00
SOLUTION
Step 1 :
In this equation, we are expected to find the x-intercept(s)
of the vertex and the co-ordinates of the vertex of the parabola :
[tex]y=x^2\text{ + 4x - 5}[/tex]Step 2 :
[tex]\begin{gathered} \text{Given y = x}^2\text{ + 4 x - 5,} \\ y=x^2\text{ + 4 x + (}\frac{4}{2})^2\text{ - 5 - (}\frac{4}{2})^2\text{ ( Completing the square method )} \\ \\ y=(x+2)^2\text{ - }9 \\ \text{The vertex of the parabola, ( h, k ) }=\text{ ( -2 , -9 )} \end{gathered}[/tex]Step 3 :
We need to solve for the x-intercepts,
[tex]\begin{gathered} \text{Given y = x}^2\text{ + 4 x - 5} \\ \text{Factorising the Quadratic Function, we have that:} \\ y=x^2\text{ - x + 5 x - 5 } \\ y\text{ = x ( x -1 ) + 5 ( x - 1 )} \\ y\text{ = ( x - 1 ) ( x + 5 )} \\ \text{Setting y = 0, we have ( x - 1 ) = 0 or ( x + 5 ) = 0} \\ x\text{ = 1 or x = -}5\text{ } \end{gathered}[/tex]CONCLUSION:
The vertex of the parabola, ( h, k ) = ( -2 , -9 )
The x - intercepts are : x = 1 or x = -5
The function f(x) is graphed below. 3 2 -5-5-3 -2 3 Using interval notation, the domain is: Using interval notation, the range is: Determine f(2)= Solve f(x) = 0 (enter as list of decimal numbers): The y-intercept is at coordinates: The x-intercepts are (enter as list of decimal coordinates): The zeros are (enter as list of decimal numbers): Over the interval [ - 4, – 2], the function is Select an answer v Over the interval [ - 2, – 1], the function is Select an answer v Over the interval ( - 1,2], the function is Select an answer v Over the interval (2, 4), the function is Select an answer v The minimum value is: The maximum value is:
Given,
The graph of the curve is shown in the question.
The domain of the function are the input value which are x coordinates values.
The range of the function are the output value which are represent by y coordinates of the graph.
So, from the graph its is clearly seen that the curve taking input from -4 to 4,
Hence, the domain of the function is,
[tex]\lbrack-4,4\rbrack[/tex]So, from the graph its is clearly seen that the curve giving output from 3 to -1,
Hence, the range of the function is,
[tex]\lbrack-1,3\rbrack[/tex]c) from the graph it is seen that when the value of x coordinate is 2 then the value of y coordinate is -1.
[tex]\text{Hence, f(2)=-1}[/tex]The value of x when the coordinates of y is 0 at x=3, -1.5.
[tex]\text{Hence, f(3)=0 and f(-1.5)=0}[/tex]The intercept of the y axis is at (0, -1).
The intercept of the x axis is at (-1.5,0) and (3,0).
The values at which y coordinate is zero is called the zeroes of the graph.
The xeroes of the graph is x=-1.5 and x=3.
In interval [-4,-2], the function is decreasing.
In interval [-2,-1] the function is decreasing.
In interval [-1,2] the function is contant.
ininterval [2,4] the function is increasing.
The maximum value of the graph is 3.
The minimum value of the graph is at -1
Algebraic proof write a reason for every step4x = 12x + 32
1. Ingrid will start college next year. She wasapproved for 10-year unsubsidized Federal Loanfor the amount of $15,000 at 4.29%a) How much interest will Ingrid accrue for 4.5 yearsnonpayment period?b) What will the new principal be when she beginsmaking loan payments?c) How much interest will she pay over the life of theloan?2. Suppose Ingrid only paid the interest during her 4years of school and the six-month grace period.What will she now pay in interest over the term ofthe loan?3. Ingrid made her last monthly interest only paymenton September 1 Her next payment is due onOctober 1. What will be the amount of interestonly payment?4. Suppose Ingrid has decided to apply for a privateloan rather then a federal loan. She has beenapproved for a 10 year loan with APR of 7.8%a) What is her monthly payments?b) What is the total amount she will pay back?c) What is total interest amount?
Given:
[tex]\begin{gathered} Principal=15,000 \\ rate(r)=4.9\%=0.049 \\ time(t)=10years \end{gathered}[/tex]To Determine: (a) How much interest will Ingrid accrue for 4.5 years non payment period
Solution
Calculate the amount accrued for 4.5years
The formula for finding amount for compound interest is
[tex]A=P(1+r)^{nt}[/tex]Substitute the given into the formula
[tex]\begin{gathered} A=15000(1+0.049)^{4.5} \\ A=15000(1.049)^{4.5} \\ A=18602.91 \end{gathered}[/tex]Step 2: Calculate the interest accrued for 4.5 years
[tex]\begin{gathered} I=A-P \\ I=18602.91-15000 \\ I=3602.91 \end{gathered}[/tex](a) Hence the interest Ingrid will accrued for 4.5 years non-payment period is $3,602.91
(b) The new principal when she begins making loan payments will be the amount accrued for 4.5years nonpayment period. This is as calculated above, which is
$18,602.91
(c) To Determine how much interest will she pay over the life of the loan
Note that the life of the loan is 10 years
[tex]So,t=10[/tex]Substitute the given into the formula for finding the amount as shown below
[tex]\begin{gathered} A=15000(1+0.049)^{10} \\ A=15000(1.049)^{10} \\ A=24201.71 \end{gathered}[/tex]Use the amount to calculate the interest of the life of the loan
[tex]\begin{gathered} I=A-P \\ I=24201.71-15000 \\ I=9201.71 \end{gathered}[/tex]Hence, the interest she would pay over the life of the loan is $9,201.71
???? help pls !$!! !!!!
Answer:
I'm pretty sure congruent means if you split them in half will they be the same shape
Step-by-step explanation:
so Yes they are congruent because if you cut a diamond in half it's going to be two triangles two triangles that are the exact same size and if you fold them they're going to be the same
Diamond form and grouping to factored form a(x-r1)(x-r2) for the first problem on the picture
Given the expression:
[tex]6x^2-13x-5[/tex]We will factor the expression as follows:
The factors of 6 = 2 x 3 or 1 x 6
The factors of 5 = 1 x 5
The difference must be = -13
So, we will use the factors of 6 = 2 x 3
So, the factoring will be as follows:
[tex]6x^2-13x-5=(3x+1)(2x-5)[/tex]We will write the expression in the form a(x-r1)(x-r2) as follows:
[tex]\frac{1}{6}(x+\frac{1}{3})(x-\frac{5}{2})[/tex]describe the transformations that occur from the parent function f(x) = x2 to the function g(x) =2(x+1)^2-7
we have
f(x)=x^2
this is a vertical parabola with vertex at (0,0)
and
we have
g(x)=2(x+1)^2-7
this is a vertical parabola with vertex at (-1,-7)
so
the transformation of f(x) to g(x) is equal to
(0,0) ------> (-1,-7)
the rule of the translation is equal to
(x,y) --------> (x-1, y-7)
that means ------> the translation is 1 unit at left and 7 units down
and we have a second transformation
(x,y) -------> (ax, y)
the factor a is 2
therefore
First transformation
x^2 --------> 2x^2
second transformation
2x^2---------> 2(x+1)^2-7
k= 12, r=4%, po=$10,000, n=25 using the compound interest formula
The compound interes formula is given by:
[tex]P_N=P_0(1+\frac{r}{k})^{Nk}[/tex]where P0 is the principal (the initial amount), r is the interes rate (in decimal form), k is the number of times the interest is compounded and N is the time elapsed.
Plugging the values given we have:
[tex]\begin{gathered} P_N=10000(1+\frac{0.04}{12})^{12\cdot25} \\ =27,137.65 \end{gathered}[/tex]Therefore the future amount is $27,137.65 and the interest earned is $17,137.65.
a ladder is leaning against the side of a brick wall the base of the ladder is 6 feet away from the brick wall the top of the ladder touches the brick wall at 8 feet from the ground how long is the ladder 4ft 10 feet or 14 feet or 7 feet
The base of ladder is at distance of b = 6 feet from the wall.
The height of top of ladder from ground is h = 8 feet.
Let the length of ladder be l.
Determine the length of ladder by using the pythagoras theorem.
[tex]\begin{gathered} l^2=(6)^2+(8)^2 \\ =36+64 \\ =100 \\ l=\sqrt[]{100} \\ =10 \end{gathered}[/tex]So length of the ladder is 10 feet.
Calculate the X value a. 4: 7 = x: 5x: 8 = 99 :5
Start writing the proportion as a fraction
[tex]\begin{gathered} 4\colon7\rightarrow\frac{4}{7} \\ x\colon5\rightarrow\frac{x}{5} \end{gathered}[/tex]then, the ratios must be the same meaning we can equal the fractions
[tex]\begin{gathered} \frac{4}{7}=\frac{x}{5} \\ \text{cross-multiply and solve for x } \\ x=4\cdot\frac{5}{7} \\ x=\frac{20}{7} \end{gathered}[/tex]repeat the same procedure for b
[tex]\begin{gathered} x\colon8\rightarrow\frac{x}{8} \\ 99\colon5\rightarrow\frac{99}{5} \\ \text{then,} \\ \frac{x}{8}=\frac{99}{5} \\ x=8\cdot\frac{99}{5} \\ x=\frac{792}{5} \end{gathered}[/tex]