36)
Triangle WVX is similar to triangle WZY. If two traingles are similar, it means that the ratio of their corresponding sides is equal. This means that
WV/WZ = VX/ZY = WX/WY
From the information given,
WX = 7, WY = a, WV = 6, VZ = a - 9
WZ = WV + VZ = 6 + a - 9 = a - 3
Thus, we have
6/(a - 3) = 7/a
By crossmultiplying, it becomes
6 x a = 7(a - 3)
6a = 7a - 21
7a - 6a = 21
a = 21
Since WY = a, then
WY = 21
this is not a graded test it my homework asap
The given expression is
100^a x 1000^b
Recall,
100 = 10^2
1000 = 10^3
Thus, the expression would be
10^2a x 10^3b
We would apply one of the rules of exponents which is expressed as
a^b x a^c = a^(b + c)
By applying this rule, we have
10^(2a + 3b)
By comparing it with 10^w, we have
w = 2a + 3b
Find the area of the figure. (Sides meet at right angles.)2 cm2 cm5 cmcmc7 cm
In the given figure, there are two squares and one rectangle.
The side of one square is , 2 cm
Therefore, the area of square is,
[tex]A_1=2^2[/tex][tex]A_1=4cm^2[/tex]The side of other square is, 5 cm.
Therefore, the area of square is,
[tex]A_2=5^2[/tex]The area of square is ,
[tex]A_2=25cm^2[/tex]Similarly, the area of rectangle is,
[tex]A_3=5\times2[/tex][tex]A_3=10cm^2[/tex]Therefore, the area of figure is,
[tex]A=A_1+A_2+A_3[/tex][tex]A=\text{ 4}+25+10[/tex][tex]A=39cm^2[/tex]The area of f
Is the point (3,-2) a solution to the system of equations?
Answer:
Explanation:
What we have to do is to make a substitution of the coordinates into the two given equations
If we have a match with the values on the right sides of the equality signs of both equations, then the point is a solution to the system
Thus, we substitute x = 3 and y = -2
We have:
[tex]\begin{gathered} 3(3)\text{ +4(-2) = 9-8 = 1} \\ 2(3)-5(-2)\text{ = 6+10 = 16} \end{gathered}[/tex]Now, as we can see, the point worked for the first equation but did not work for the second
Ultimately, what that means is that the point is not a solution to the system of equations
To find the measure of
Let us first get the value of z,
[tex](2z-3)^0+(5z-6)^0=180^0[/tex][tex]\begin{gathered} 2z-3^0+5z-6^0=180^0 \\ \text{collec like terms,} \\ 2z+5z-3^0-6^0=180^0 \end{gathered}[/tex][tex]\begin{gathered} 7z-9^0=180^0 \\ 7z=180^0+9^0 \\ 7z=189^0 \end{gathered}[/tex][tex]\begin{gathered} z=\frac{189^0}{7} \\ z=27^0 \end{gathered}[/tex]Hence, the value of z is 27°.
Let us now solve for the measure of angle M,
[tex]m\angle M=(5z-6)^0[/tex][tex]\begin{gathered} \text{where z=27}^0 \\ \text{substitute the value of z into the expression and find the angle M} \end{gathered}[/tex][tex]m\angle M=(5\times27-6)^0[/tex][tex]\begin{gathered} =135^0-6^0 \\ m\angle M=129^0 \end{gathered}[/tex]Hence, the value of the measure of angle M is 129°.
iDentify the equation of the circle that has its center at (-27, 120) and passes through the origin A. (x−27)^2+(y+120)^2=123 B. (x+27)^2+(y−120)^2=123 C. (x−27)^2+(y+120)^2=15129 D. (x+27)^2+(y−120)^2=15129
The equation of a circle with radius r centered at (h,k) is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]If the circle passes through the origin, then we have:
[tex]r^2=h^2+k^2[/tex]Then, for a circle centered at (-27,120) passing through the origin, we have:
[tex]\begin{gathered} r^2=(-27)^2+120^2 \\ r^2=15129 \\ (x+27)^2+(y-120)^2=15129 \end{gathered}[/tex]Answer: D
find the value of X that would prove j || k. state the converse that justifies your answer.
Let's begin by listing out the given information:
Lines j & k are parallel. Both are intersected by a transversal line
Both angles in the picture are congruent. As such, the value of x is:
[tex]\begin{gathered} 14x-25=129 \\ 14x=129-25 \\ 14x=104 \\ x=\frac{104}{14}=7.4286\approx7.43 \\ x\approx7.43 \end{gathered}[/tex]The converse of j || k is k || j (k is parallel to j)
h + 1.8 =11.9 and how do I check my answer on that
EXPLANATION
Given the equation h + 1.8 = 11.9
Subtracting -1.8 to both sides:
h = 11.9 - 1.8
Adding like numbers:
h = 10.1
We can check the answer by substituting on the equation as follows:
10.1 + 1.8 = 11.9
Adding numbers:
11.9 = 11.9
As the numbers are equal, the equation is well done.
Select the interval where g is negativeA:2< x < 3B: 3 < x < 4C: 4 < x < 5D: none of the above
To select the interval where g is negative:
From the graph,
We observe that
The interval where g is negative is,
[tex]-4So, the correct option is,[tex]2Therefore, the co4Solve each problem to color the picture! Type your answers in the box56.78Orange The worlds tallest house ofcards measured 8 meters tall and wasbuilt in Dallas, Texas. There areapproximately 5 meters in 16 feet.What was the heightof the house ofcards in feet?91011121315Yellow30Purple 10.517Green35Red2419Blue228.6Orange
Since the given information says, there are approximately 5 meters in 16 feet, we need to find the height in feet of the house of cards which is 8 meters tall
We need to find X in feet.
X = 8 * 16 / 5 = 25.6 ft
The pair of square pyramids are similar. Use the given information to find the scale factorof the smaller square pyramid to the larger square pyramid.The scale factor is :)(Type whole numbers.)
If the scale factor of one figure to another one is k, then the ratio of their volumes is equal to:
[tex]k^3[/tex]The volume in cubic inches of the smaller pyramid is 27, while the volume of the bigger pyramid is 343. Then:
[tex]k^3=\frac{27}{343}[/tex]Take the cubic root to both members of the equation to isolate k:
[tex]\begin{gathered} \Rightarrow k=\sqrt[3]{\frac{27}{343}} \\ =\frac{\sqrt[3]{27}}{\sqrt[3]{343}} \\ =\frac{3}{7} \end{gathered}[/tex]Therefore, the scale factor of the smaller pyramid to the larger pyramid, is:
[tex]\frac{3}{7}[/tex]Please explain how to solve this problem and Please explain step by step explanation.
Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval.
f (x) = x3 - 2x2 + 16x + 28; [4, 5]
A Yes
B No
==========================================================
Explanation:
The interval we're working with is [4,5] aka [tex]4 \le \text{x} \le 5[/tex]
We'll plug the endpoints of said interval into the f(x) function
Let's start with x = 4
[tex]f(\text{x}) = \text{x}^3-2\text{x}^2+16\text{x}+28\\\\f(4) = (4)^3-2(4)^2+16(4)+28\\\\f(4) = 124\\\\[/tex]
The actual result doesn't matter. All we care about is if the value is positive or negative. We see that f(4) is positive.
Now plug in x = 5
[tex]f(\text{x}) = \text{x}^3-2\text{x}^2+16\text{x}+28\\\\f(5) = (5)^3-2(5)^2+16(5)+28\\\\f(5) = 183\\\\[/tex]
The value of f(5) is positive as well.
Unfortunately we don't have enough info to determine if f(x) has a root in the interval [4,5]
We would need either of the following conditions
f(4) negative and f(5) positivef(4) positive and f(5) negativeIn other words, we need the signs of f(4) and f(5) to alternate. One needs to be positive, the other negative. This is to guarantee that the f(x) curve crosses the x axis at some point. Think of it like a river or a road. The continuous road can't magically jump over the x axis without crossing it.
But because f(4) and f(5) don't differ in sign, this means we don't know if f(x) ever dips below the x axis. It might as shown in figure 1, but it may not as indicated in figure 2. There's simply not enough information.
Please help me with this question thank you very much
The equations are equivalent by the equality property of addition, which states that if we add the same quantity to both sides of an equation, then our equation remains the same. Since john is adding n to both sides, the equation remains the same and therefore, they are equivalent.
HELP ME PLEASEEEEEEEEEEEEE
Answer: B At most 45 cakes
Step-by-step explanation:
Given, 5x + 15 ≤ 240
⇒ x + 3 ≤ 48 [Dividing by 5 on both sides]
⇒ x ≤ 45 [Subtracting 3 from both sides]
that means the bakery makes less than or equal to 45 cakes. the most cakes they can make is 45. So they make at most 45 cakes a day
1024 km are equal to how many cm?
Answer:
1024 km are equal to 102400000 cm
Explanation:
There are a hundred thousand centimeters in one kilometer, this would help us convert 1024 km to cm, as required.
Let x denote the value of 1024 km in cm.
1 km = 100000 cm
1024 km = x cm
Then we have:
x = 1024 * 100000
= 102400000
Therefore, there are 102400000 cm in 1024 km.
The two polygons are similar. Write a proportion and solve for x. I just need help with 13
EXPLANATION
The appropiate relationship is
[tex]\frac{x}{3}=\frac{6}{4}[/tex]Multiplying both sides by 3:
[tex]x=3\cdot\frac{6}{4}[/tex]Simplifying terms:
[tex]x=\frac{9}{2}[/tex]The answer is x=9/2 or 4.5
Lesson 3 Problem-solving Practice Adding Linear Expressions 2. Heather was building a scale model of the Pentagon for her history class. 7" P= (246) 3. A mailing st mailing env a variety of 4 centimete Write and the perime (2x + 3) in a. Write and simplify an expression to represent the perimeter of Heather's scale model. 4. Find the perimete b. Find the perimeter of the model if x = 2:
Since a pentagon is 5 sided, the perimeter would be:
[tex]5(2x+3)\rightarrow10x+15[/tex]Using x = 2 , we would get:
[tex]10(2)+15=20+15=35[/tex]m arc Ab=80°find the length
Solution
For this case we know the diameter:
D= 9 ft
Then the radius is:
r= 9/2 ft
Then we can use the following formula
[tex]\text{mAB}=2\pi r(\frac{\theta}{360})[/tex]Then the measure would be:
[tex]\text{mAB}=2\pi\cdot\frac{9}{2}(\frac{80}{360})=2\pi[/tex]The denominator of a fraction is one more than three times
Given:-
The denominator of a fraction is one more than three times and if 8 is added to the neumerator and the demominator then the solution is 1/2.
To find the equation.
So now the given fraction is,
[tex]\frac{x}{1+3x}[/tex]So now we add. so we get,
[tex]\frac{x+8}{1+3x+8}=\frac{1}{2}[/tex]So now we get,
[tex]\frac{x+8}{3x+9}=\frac{1}{2}[/tex]So this is the required solution.
When Steve woke up his temperature was 102 F. Two hours later is was 3 degrees lower. What is his temperature now?
1) Considering that when He woke up the temperature was 102ºF and then there was a decrease in the temperature by 3º we can write out the following:
[tex]102^{\circ}-3^{\circ}=99^{\circ}[/tex]Note that the temperature decreased by exactly 3º.
2) Hence, the answer is 99ºF
The point (4,3) is rotated 180° about the origin. What are the coordinates of this point after therotation?
ANSWER:
(-4, -3)
STEP-BY-STEP EXPLANATION:
We have the following point:
[tex](4,3)[/tex]A 180° rotation complies with the following rule:
[tex]\begin{gathered} P(x,y)\rightarrow P^{\prime}(-x,-y) \\ \text{therefore, in this case:} \\ (4,3)\rightarrow(-4,-3) \end{gathered}[/tex]The point after the rotation is (-4, -3)
What is the formula if the speed is missing? *A. s=t/dB. s=d/tC. s=t+dD. s=d x tFind the area of a trapezoid with bases of 4cm and 6cm, height of 5cm? *A. 120 sq.cmB. 60 sq.cm.C. 50 sq.cm.D. 25 sq.cm.
Answer:
Explanations:
Sasha goes to buy groceries. She buys two packages of corn (99€ per package),three gallons of milk ($2.90 per gallon), and a loaf of bread ($1.29). She givesthe clerk $20.00 for her purchases. How much change does Sasha get back?
First, multiply the price of each item by the number of items to find the total amount of money spent on each:
2 packages of corn for $0.99 each
[tex]2\times0.99=1.98[/tex]3 gallons of milk for $2.90 each
[tex]3\times2.90=8.70[/tex]A loaf of bread: $1.29
Then, add all the quantities to find the total price for all the purchases:
[tex]1.98+8.70+1.29=11.97[/tex]Substract the total price of the purchases from $20.00 to find the amount of change that Sasha gets back:
[tex]20.00-11.97=8.03[/tex]Therefore, the amount of money that she gets back, is:
[tex]8.03[/tex]what is the equation (05) (3,0)
Which of the folding statements of true of the functions below? F(x)=(x-1)(x-3)2(x-3)2
a) the multiplicity of x=3, or (x-3), is 2. That means, this zero repeats twice.
b) one of the roots is x=3, not x=-3
c) odd function: f(-x)=-f(x)
f(-x) = (-x-1)^2(-x-3)^2
(x^2 + 2x + 1 ) (x^2 +6x +9)
-f(x)=-(x-1)^2(x-3)^2
=-(x^2-2x+1)(x^2-6x+9)
f(-x) is not equal as -f(x)
d) If we graph the function, we will see that it range is y>0
For this reasion, statement A is true.
Which of the following is the standard equation of the ellipse with vertices at (3, 0) and (13, 0) and an eccentricity of four fifths question mark
quantity x minus 8 end quantity squared over 25 plus y squared over 9 equals 1
quantity x plus 8 end quantity squared over 9 plus y squared over 25 equals 1
quantity x minus 8 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 8 end quantity squared over 64 plus y squared over 100 equals 1
The ellipse equation is given by option a: quantity x minus 8 end quantity squared over 25 plus y squared over 9 equals 1.
What is termed as the ellipse?An ellipse does have an eccentricity less than one and reflects the locus of points whose distances from the ellipse's two foci are a constant value. The shape of the an egg in two dimensions and running monitoring in a sports stadium are two simple examples of ellipses in our daily lives.The equation for an ellipse of centre is:
(x - x₀)²/a² + (y - y₀)²/b² = 0.
The values a and b are determined by the vertices and eccentricity.
That has vertices at (3, 0) and (13, 0) , resulting in:
x₀ = 13 + 3 / 2 = 8
y₀ = 0 + 0 /2 = 0
a = 13 - 3/2 = 5
a² = 25
It has the eccentricity of 4/5, so:
4/5 = c/a
c = 4
Thus, b is given by the following equation:
c² = a² - b²
b² = a² - c²
b² = 25 - 16
b² = 9
The ellipse's equation is:
(x - 14)²/25 + (y )²/9 = 1.
Thus, the equation of ellipse is "quantity x minus 8 end quantity squared over 25 plus y squared over 9 equals 1."
To know more about the ellipse, here
https://brainly.com/question/16904744
#SPJ1
the figure Shown is the base of a right solid that is 10 meters high corners that look square are square find the latter will surface of the solid dimensions are in metres
let's find the area by parts
red is the first part
we need the area of the red square an substract the mid-circle area
square is A=bxh
so A=2x4=8
the area of the circle is A=pi x r2
so the area of the circle is A=pi x 4 and the middle is 2pi
the total red area is
[tex]\begin{gathered} Ar=8-2\pi \\ \end{gathered}[/tex]green part
te area is A=bxh, the heigth is 4 like the diameter of the circle and the base is 8 less 2 (of the radius) and less 4(of the base
x² + 2x = 0 To resolve
we have the quadratic equation
[tex]x^2+2x=0[/tex]Solve the quadratic equation
Solve by factoring
Factor x
[tex]x(x+2)=0[/tex]The values of x are
x=0x=-2I keep getting kicked out every time a tutor goes to answer my question.
(C) translation 8 units right
Explanationgiven the fuction:
[tex]f(x)=x[/tex]was transformed to obtain
[tex]g(x)=x-8[/tex]so, the transformation to the patern function was subtract 8
Step 2
when you subtrac a value k to the function´s argument the function is shifted to the rigth, so the answer is
(C) translation 8 units right
I hope this helps you
Find the volume of the figure.
3 m
3 m
3 m
Answer:
27m
Step-by-step explanation:
this sounds like a cube so we multiply all these numbers together
3x3=9
9x3=27
Please mark brainliest have a nice day
As the number of years decreases from 2 to 1 in the following graph, does the population increase, decrease, or remain the same?
Given the graph of Time Vs. Population, you can identify that the x-axis represents the Time (in years), and the y-axis represents Population (in thousands),
Notice that, in this case, when:
[tex]x=2[/tex]The corresponding y-value is:
[tex]y=4[/tex]And when:
[tex]x=1[/tex]The y-value is:
[tex]y=6[/tex]Therefore, you can identify that as the number of years decreases from 2 to 1, the population increases.
Hence, the answer is: First option.